y^2=1/5(x-4), (24,2)

In the year 1582, January 1st was adopted for the new year celebration

An equation is used to show the relationship between numbers and variables.

Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction. The degree of a polynomial determines it type such as linear, quadratic, cubic and so on.

The polynomial having a degree of 3 is cubic while that with a degree of 2 is quadratic and that with degree of 1 is linear

The year that January 1st was adopted as new year can be gotten using the function:

f(x) = 3x³ - 7x² - 5x + 7

f(9) gives the year that it was adopted. Substituting x = 9 gives:

f(9) = 3(9)³ - 7(9)² - 5(9) + 7

f(9) = 1582

In the year 1582, the new year was celebrated at January 1st

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The coordinates of vertex D in the parallelogram ABCD are (7,-3).

In a parallelogram, opposite sides are parallel and congruent. Therefore, the vector that goes from vertex A to vertex B is the same as the vector that goes from vertex C to vertex D, and the vector that goes from vertex B to vertex C is the same as the vector that goes from vertex D to vertex A.

The vector from vertex A to vertex B is [tex]< 5-(-3), 7-1 > = < 8,6 >[/tex]

So, the vector from vertex C to vertex D is also [tex]< 8,6 >[/tex]

The vector from vertex B to vertex C is [tex]< 6-5, 2-7 > = < 1,-5 >[/tex]

So, the vector from vertex D to vertex A is also [tex]< 1,-5 >[/tex]

To find the coordinates of vertex D, we can add the vector from vertex C to vertex D to the coordinates of vertex C.

The coordinates of vertex C are (6, 2)

So, the coordinates of vertex D are [tex](6+1, 2-5) = (7, -3)[/tex]

Therefore, the coordinates of vertex D in the parallelogram ABCD are (7,-3).

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Answer:

+4

Step-by-step explanation:

if x is your number, then x+4 is four more than

Answer:

Answer Below

Step-by-step explanation:

The phrase "4 more than" means 4 has been added onto a number. Eg:"Sue has 4 more sweets than Ann, means that however many sweets Ann has, Sue's number is bigger by 4.

By using simple arithmetic and using calculator we get:

a. 1/4 • (-12) = (-3)

b. -1/3 • 39 = -13

c. (-4/5) • (-75) = 60

d. -2/5 • (-3/4) = 3/10 = 0.3

e. 8/3• -42 = -56

Arithmetic is a branch of mathematics that deals with the manipulation of numbers and their properties. It is the study of numbers and the operations that can be performed on them, such as addition, subtraction, multiplication, and division. Arithmetic also includes concepts such as fractions, decimals, and percentages. The study of arithmetic is fundamental to many other branches of mathematics, including algebra, geometry, and calculus, as well as many practical fields like finance, engineering, and computer science.

A calculator is a device that performs mathematical calculations. It can be a handheld device or a software program on a computer or mobile device. Calculators typically have buttons or keys for performing basic arithmetic operations, such as addition, subtraction, multiplication, and division, as well as more advanced functions like trigonometry and logarithms. Some calculators also have the ability to store and recall numbers, perform conversions between units of measurement, and perform other specialized functions.

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Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

What are linear equations?

A linear equation is a mathematical equation that can be written in the form of Ax + By = C, where A, B and C are constants and x and y are variables.

Let's call the number of pages that both friends read x. We know that Julie's reading speed is 3 pages per minute and Cassie's reading speed is 2 pages per minute.

We can set up the equation:

x = 3t + 9 (where t is the time in minutes that Julie takes to read x pages)

x = 2t + 35 (where t is the time in minutes that Cassie takes to read x pages)

We know that they read the same number of pages, so we can set the two equations equal to each other:

3t + 9 = 2t + 35

We can then solve for t:

t = 26 minutes

So it took them 26 minutes to read the same number of pages. We can use that value to find the number of pages that they read:

x = 3t + 9 = 3(26) + 9 = 79 pages

Hence, Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

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Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

What are linear equations?

A linear equation is a mathematical equation that can be written in the form of Ax + By = C, where A, B and C are constants and x and y are variables.

Let's call the number of pages that both friends read x. We know that Julie's reading speed is 3 pages per minute and Cassie's reading speed is 2 pages per minute.

We can set up the equation:

x = 3t + 9 (where t is the time in minutes that Julie takes to read x pages)

x = 2t + 35 (where t is the time in minutes that Cassie takes to read x pages)

We know that they read the same number of pages, so we can set the two equations equal to each other:

3t + 9 = 2t + 35

We can then solve for t:

t = 26 minutes

So it took them 26 minutes to read the same number of pages. We can use that value to find the number of pages that they read:

x = 3t + 9 = 3(26) + 9 = 79 pages

Hence, Julie read 79 pages after 26 minutes and Cassie read 79 pages after 26 minutes.

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The dimensions of the original sandbox was 2 ft X 2 ft..

Let, The original has a length of Xft and a width of Xft

The area of original sandbox is X^2 ft^2

As per given statement,

The new sandbox would have a length of (X+4)ft and a width of (X+5)ft

So, the area of new sand box would be: (X+4)(X+5) ft^2

Given, the area of new sandbox will be 38 square feet greater than the area of the original sandbox.

so,

X^2+38 = (X+4)(X+5)

or, X^2+38 = X^2 + 9X + 20

Eliminating X^2 from both side

0r, 9X+ 20 = 38

0r, 9X = 18

0r, X = 18/9 = 2

So, we assumes that the original has a length of Xft and a width of Xft

then the dimensions of the original sandbox was 2 ft by 2 ft.

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In this equation, n represents the original price of the television before the sale.

Equation is a mathematical statement that expresses the equality of two expressions by using numbers, symbols, and operations. It is used to describe the relationship between different variables in a problem. Equations are usually written as a statement of equality, such as 2 + 2 = 4, where the left side of the equation (2 + 2) is equal to the right side (4). Equations can be used to solve for a single unknown value, or to determine the relationship between multiple variables.

In this equation, n represents the original price of the television before the sale.

This means that the original price of the television was $375.

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The factors of 5x as calculated from the data given is found to be as 5, x and  1 .

On factorizing 5x we can write it as ,

5 x 1 x x .

Therefore the factors are 5 , 1 and x.

There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.

The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.

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Answer:

16 ounces = 1 pint, 8 times 2 = 16

Step-by-step explanation:

Answer in explanation:

1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.

(8 x 2 = 16

your answer is 2

Hope this helps!

Answer: Sara's mean quiz score is 12

Step-by-step explanation:

Mean is the Sum of the Terms divided by the number of terms.

If we add up every score we get 60, we then will divide this by how many scores there were (5).

60/5 = 12

The experimental probability is 30% higher than the predicted probability.

What is meant by experimental probability?

Experimental Probability: what actually occurs when the experiment is carried out. For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.

The spinner has 10 sections and a 10% chance of landing on the section representing rain. Therefore, the probability of rain predicted by the spinner is 0.1 or 10%.

From the simulation, the results are 3, 6, 1, 8, and 3. Out of these 5 spins, 2 of them landed on the section representing rain (1, 3). Therefore, the experimental probability of rain from the simulation is 2/5 or 40%.

The difference between the experimental probability from the simulation and the prediction is the difference between the two percentages, which is:

(experimental probability) - (predicted probability) = 40% - 10% = 30%

Hence, the experimental probability is 30% higher than the predicted probability.

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A homogenous mixture of two or more components is referred to as a solution.

Solution Examples: Brass is an illustration of a solid solution. Liquid solutions include aqueous hydrochloric acid as an illustration (HCl in water). Air is an illustration of a gaseous solution.

1)When we combine salt (often table salt) and water, we create salt water.

2)By combining sugar and water, sugar water is created.

3)Mouthwash is made up of various chemicals that have been dissolved in water.

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Answer:

Function Domain and Range

g(x)=\sqrt{x} -5

what is the range and domain

To find the range of g(x), we can substitute a few values of x into the expression for g(x) to see what the output is. For example, when x = 0, g(x) = sqrt(0) - 5 = 0 - 5 = -5. When x = 1, g(x) = sqrt(1) - 5 = 1 - 5 = -4. When x = 2, g(x) = sqrt(2) - 5 = 1.4142 - 5 = -3.5858.

As we can see, the output of g(x) is always a negative number for any value of x in the domain. Therefore, the range of g(x) is the set of all negative real numbers, or (-infinity, 0).

So, the domain of g(x) is all real numbers x such that x >= 0, and the range of g(x) is all negative real numbers (-infinity, 0).

Answer:

1. 6
2. 15

Step-by-step explanation:

4 pumpkins: $32
=> 1 pumpkin = 32 : 4 = $8
- He will have to sell 48 : 8 = 6 pumpkins to make $48

- He sold: 120 : 8 = 15 pumpkins that day

The relationship exists between N and K are the endpoints of the side KN.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions.

It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.

we know that for a parallelogram KLMN is a quadrilateral whose two sides are parallel to each other and has two non-parallel sides.

for N and K we could say that the two are endpoints of the line segment KN; which is one of a side of a parallelogram KLMN.

Therefore, The relationship exists between N and K are the endpoints of the side KN.

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So, Todd picked 1 apple.

We can use the information given to set up the following equations:

Let x be the number of apples Jack picked, and y be the number of apples Marta picked.

We know that x + y = 16 (Jack and Marta pick a total of 16 apples)

Let y be the number of apples Marta picked, and z be the number of apples Rand picked.

We know that y + z = 15 (Marta and Rand pick a total of 15 apples)

Let z be the number of apples Rand picked, and w be the number of apples Todd picked.

We know that z + w = 13 (Rand and Todd pick a total of 13 apples)

We know that the total number of apples picked is 45, therefore x + y + z + w = 45

We can use the equation x + y = 16 to express x in terms of y:

x = 16 - y

We can substitute this into the other equations

(16 - y) + y = 16

y + z = 15

z + w = 13

We can sum all the equations:

(16 - y) + y + y + z + z + w = 45

16 + 2y + 2z + w = 45

From the equation y + z = 15, we can substitute y = 15 - z

16 + 2(15 - z) + 2z + w = 45

16 + 30 - 2z + 2z + w = 45

46 + w = 45

w = 1

Therefore Todd picked 1 apple.

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1. To maximize the profit :

28 jars of salsa and

0 jars of tomato sauce should be made.

which  make maximum profit of $42.

2.  In order to maximize the total monthly profit

2300 units of T₁ type table and and

600 units of T₂ type table should be made

which provide maximum profit of $273000.

In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.

1. Let x be the numbers of jars of tomato sauce

Let y be the number of jars of salsa sauce

Profit P(x, y)=2x+1.5y

x≥0

y≥0

10x+5y≤140

x + y ≤13

​The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.

A at (0,13)

B at (0,28)

C at (14,0)

D at (15,0)

E at (15, -2)

Evaluate profit P(x, y) at each vertex

A at (0,13):P(0,13)=$19.5

B at (0,28):P(0,28)=$42

C at (14,0):P(14,0)=$28

D at (15,0):P(15,0)=$30

E at (15, -2):P(15,-2)=30-3=$27

The maximum profit of $42 is at vertex B.

Which means production of 28 jars of salsa and 0 jars of tomato sauce provides maximum profit of $42.

2. Let x be the number of tables of type T₁

​and y the number of tables of type T₂

​Profit P(x, y)=90x+110y

x≥0

y≥0

2x+4y≤7000

x+2.5y≤4000

2x+1,5y≤5500

​The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.

A at (0,0)

B at (0,1600)

C at (1500,1000)

D at (2300,600)

E at (2750,0)

Evaluate profit P(x, y) at each vertex

A at (0,0):P(0,0)=0

B at (0.1600):P(0,1600)=90(0)+110(1600)=176000

C at (1500,1000):P(1500,1000)=90(2500)+110(1000)=245000

D at (2300,600):P(2300,600)=90(2300)+110(600)=273000

E at (2750,0):P(2750,0)=90(2750)+110(0)=247500

The maximum profit of $273000 is at vertex D.

which means production of 2300 tables of type T₁ and 600 tables of type T₂ makes maximum  profit.

1. Hence, maximum profit is made by making

28 jars of salsa and

0 jars of tomato sauce getting

$42 of profit.

2. Hence the company needs to produce

2300 tables of type T₁ and

600 tables of type T₂,

in order to maximize its monthly profit which is equal to $273000.

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Answer: 5$ for 52 days

Step-by-step explanation: (5 x 52) + 90 = 350

Therefore , the solution of the given problem of function comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and

Domain :[ -∞,0 ] U [ 0,∞].

According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.

Here,

Part A:

=> 4/6x² - 5x²/4x

=> 8 - 15x + 3x³/12x²

=>  3x³- 15x +8 / 12x²

=> x(3x²- 15 ) + 8 / 12x²

Part B:

Domain : x ∈ R : x≠ 0

Part c:

The function domain at x= 0 Domain :[ -∞,0 ] U [ 0,∞]

Therefore , the solution of the given problem of equation comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and Domain :[ -∞,0 ] U [ 0,∞].

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This is a triangle whose three angles are in the ratio 1:2:3 and respectively measure 30° ( π/6), 60° ( π/3), and 90° ( π/2) and the sides are in the ratio 1:√3: 2.

These triangles are also known as special right triangles, such as 30-60-90 triangles, and 45°-45°-90° triangles. Among all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs, √2/4.

The 30°-60°-90° triangle is the right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. By dividing by 3, the angle α + δ must be 60°. The right angle is 90°, and the remaining angle is 30°.

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The graph is attached and  the point of maximum as y"(π/6) < 0 and at point of minimum y"(π/2) > 0.

An inflection point is where a graph's curvature changes, from concave up to concave down or vice versa. It is also known as a turning point, flex, inflection, or "point of diminishing returns."

A concave down graph resembles an upside-down U or a cap, while a concave up graph resembles the letter U (or a "cup"). The intersection of a "cup" and a "cap" marks the inflection point.

Given displacement of mass by function,

y = sin(3t), where 3t is in radians,

the graph for t = 0 and t = 2 sec.

2: The position of turning point,

differentiate the equation we get,

y' = 3cos(3t)

the turning points are t = π/6 and t = π/2

y'(π/6) = y'(π/2) = 0

3: inflexion points,

again differentiate the equation we get,

y" = -9sin(3t)

and inflection at π/3

because y"(π/3) = 0

Maximum and minimum points are π/6 and π/2 respectively,

as the point of maximum t = π/6 as y"(π/6) < 0,

and point of minimum at t = π/2 as y"(π/2) > 0.

Hence the graph is attached and maximum at t = π/6, and minimum at t = π/2, and inflection at π/3.

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When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5.

The link between two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.

The definition an equation in algebra is a mathematical expression that indicates the equivalence of two mathematical terms. In equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal."

When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5, this represents the situation where m is Merida's age.

correct option: D

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Answer:

[tex]b = 90[/tex]

[tex]d = 100[/tex]

[tex]c = 80[/tex]

Step-by-step explanation:

The problem is asking for the values of the variables [tex]b[/tex], [tex]c[/tex], and [tex]d[/tex] in the given parallelogram with angles [tex]d\textdegree[/tex], [tex]c\textdegree[/tex], [tex](b-10)\textdegree[/tex], and [tex](b+10)\textdegree[/tex].

To solve for these variables, we can construct three equations using the knowledge that any two adjacent angles of a parallelogram are supplementary (their measures add to 180º).

The first equation shows that the top two angles are supplementary:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

The second equation shows that the bottom two angles are supplementary:

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

The third equations shows that the left two angles are supplementary:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

First, we can solve for [tex]b[/tex] in the second equation using simple algebraic manipulation.

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

[tex](b+b)\textdegree + (10-10)\textdegree = 180\textdegree[/tex]

[tex]2b\textdegree = 180\textdegree[/tex]

[tex]b\textdegree = 90\textdegree[/tex]

[tex]b = 90[/tex]

Using this [tex]b[/tex]-value, we can solve for [tex]d[/tex] by rewriting the third equation, plugging [tex]90[/tex] in for [tex]b[/tex]:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + (90-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + 80\textdegree = 180\textdegree[/tex]

[tex]d\textdegree = 100\textdegree[/tex]

[tex]d = 100[/tex]

Finally, we can solve for [tex]c[/tex] in the first equation by plugging [tex]100[/tex] in for [tex]d[/tex]:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]100\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]c\textdegree = 80\textdegree[/tex]

[tex]c = 80[/tex]

Arithmetic sequences are those in which the difference between each subsequent phrase is a fixed number. This is shown by writing the equation for a line as y = mx+c, where m denotes the slope and c the y-intercept.

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As per the given equation the total number of positive divisors that $6$ has is 38.

The divisors (or factors) of a positive integer are the integers that evenly divide it.

The formula for calculating the total number of divisor of a number ′n′ where n can be represent as powers of prime numbers is shown as.

If N= paqbrc

Then total number of divisors = (a+1)(b+1)(c+1).

If we want to find the positive divisors for an integer n, we just take the integers 1, 2, 3, . . . , n, divide n by each, and those that divide evenly make up the set of positive divisors for n.

The divisors (or factors) of a positive integer are the integers that evenly divide it

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The equation of the line in slope-intercept form, with the point (4, -5) and an undefined rate of change is x = 4.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, any line that has an undefined slope (rate of change) is a vertical line because it does not have a y-intercept. This ultimately implies that, a vertical line that is parallel to the y-coordinate (y-axis) would have an undefined slope (rate of change).

Generally speaking, the equation of a line that has an undefined slope (rate of change) is given by this mathematical expression;

x = a

Where:

a represents the x-intercept.

At point (4, -5), the required equation with an undefined slope (rate of change) is x = 4.

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a) After 8 hours, a person earned $148 in wages.

The function is, $x = 18.5 y

b) The linear function to represent the table is, y = 10x -4

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                         = 18.5

So, if y represents the number of hour and $x the wages, then the function is

$x = 18.5 y

b) The unit rate change for the function is

= (56-36)/(6-4)

= 20/ 2

= 10

So, the linear function to represent the table is

y - 36 = 10(x - 4)

y- 36 = 10x - 40

y = 10x -4

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Answer:

150 of 400 can be written as:

150400To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

150400 × 100100= (150 × 100400) × 1100 = 37.5100Therefore, the answer is 37.5%

If you are using a calculator, simply enter 150÷400×100 which will give you 37.5 as the answer.

The area of the given shape is 46 cm²

Formulas used:

Area of the triangle = (1/2) × Base × Height

Area of rectangle = Base × Width

Here we have  

The composite figure with a right-angled triangle and a rectangle

In a right-angled triangle,

The base of the triangle = 3 cm

Height of the triangle = 4 cm

Area of the triangle

= (1/2) × base × height

= (1/2) × 3 × 4

=  (1) × 3 cm × 2 cm

=  6 cm²  

In rectangle,

Length of the rectangle = 10 cm

Width of the rectangle = 4 cm

Area of the rectangle

= Length × Width

= 10 cm × 4 cm

= 40 cm²

By the above calculations,

Area of the given figure = Area of triangle + Area of rectangle

= 6 cm² + 40 cm² = 46 cm²

Therefore,

The area of the given shape is 46 cm²

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To convert the log2 to log10, we can use the convert of base formula for logarithms. The change of base formula for logarithms is as written:

log b(x)=logc(x) / logc(b)

By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:

log2(x)=log10(x)/log10(2) = log(x)/log (2)

This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.

The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is presented as “log e e”.

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