Intro To Logs Quiz 1

1. Log a + log b + log cCondense this logarithmic expression.

Log a+b+c

Log abc

Log a + b + c

Condensing is the reverse process of expanding. So when logarithms in the expanded form are added, they are multiplied in the condensed form, giving you the answer log abc, where a, b, and c are multiplied, not added.

Explanation

Condensing is the reverse process of expanding. So when logarithms in the expanded form are added, they are multiplied in the condensed form, giving you the answer log abc, where a, b, and c are multiplied, not added.

2. Write the equation 5³ = 125 in log form.

Log 3 (125) = 5

Log 125 (5) = 3

Log 5 (125) = 3

Log 5 (3) = 124

The equation 53 = 125 can be written in log form as log 5 (125) = 3. This is because log 5 (125) means "the exponent to which 5 must be raised to give 125" and this exponent is equal to 3.

Explanation

The equation 53 = 125 can be written in log form as log 5 (125) = 3. This is because log 5 (125) means "the exponent to which 5 must be raised to give 125" and this exponent is equal to 3.

3. Write the log equation log ₂32 = 5 in exponential form

2 ^ 5 = 32

5 ^ 2 = 32

2 ^ 32 = 5

32 ^ 2 = 5

The given log equation log 2 32 = 5 can be written in exponential form as 2 ^ 5 = 32. This means that 2 raised to the power of 5 equals 32.

Explanation

The given log equation log 2 32 = 5 can be written in exponential form as 2 ^ 5 = 32. This means that 2 raised to the power of 5 equals 32.

4. Solve . Round to 4 decimal places.

0.7442

1.3437

0.4472

-0.4472

The given numbers are 0.7442, 1.3437, 0.4472, and -0.4472. The question asks to solve, but it is not clear what operation or equation needs to be solved. Without further information, it is not possible to determine the correct answer or provide an explanation.

Explanation

The given numbers are 0.7442, 1.3437, 0.4472, and -0.4472. The question asks to solve, but it is not clear what operation or equation needs to be solved. Without further information, it is not possible to determine the correct answer or provide an explanation.

5. Write the equation in logarithmic form: 4⁴=256

Log256 4=4

4log 256=4

256log 4=4

Log4 256=4

4 is the base in the expression 4^4 as well as the base in the logarithm. 256 is the product and the last 4 is the exponent.

Explanation

4 is the base in the expression 4^4 as well as the base in the logarithm. 256 is the product and the last 4 is the exponent.

6. A logarithmic function is the inverse of which function?

Quadratic

Linear

Cubic

Exponential

A logarithmic function is the inverse of an exponential function. This means that if we have a value x and we apply an exponential function to it, we get y. The logarithmic function will take y as input and return x. In other words, the logarithmic function "undoes" the effect of the exponential function. This relationship between logarithmic and exponential functions is important in various mathematical and scientific applications.

Explanation

A logarithmic function is the inverse of an exponential function. This means that if we have a value x and we apply an exponential function to it, we get y. The logarithmic function will take y as input and return x. In other words, the logarithmic function "undoes" the effect of the exponential function. This relationship between logarithmic and exponential functions is important in various mathematical and scientific applications.

7.

log

ab
c

Expand this logarithmic expression.

Log a + log b − log c

Ab/c

Log a x log b / log c

Log a + log b + log c

Log a - log b + log c

When you multiply or divide within a logarithmic expression, it is added or subtracted in the expanded form. Therefore log a + log b − log c is the answer.

Explanation

When you multiply or divide within a logarithmic expression, it is added or subtracted in the expanded form. Therefore log a + log b − log c is the answer.

8. The equation 2 ^x = 9 can be entered in the calculator in which form?

(log 9) / (log 2)

Log 9 * log 2

(log 9 )^2

(log 2) / (log 9)

The equation 2x = 9 can be entered in the calculator in the form (log 9) / (log 2) because this equation represents a logarithmic expression. By taking the logarithm of both sides of the equation, we can isolate the variable x. The logarithm of 9 to the base 2 will give us the value of x that satisfies the equation. Therefore, entering the equation in the form (log 9) / (log 2) in the calculator will help us find the value of x.

Explanation

The equation 2x = 9 can be entered in the calculator in the form (log 9) / (log 2) because this equation represents a logarithmic expression. By taking the logarithm of both sides of the equation, we can isolate the variable x. The logarithm of 9 to the base 2 will give us the value of x that satisfies the equation. Therefore, entering the equation in the form (log 9) / (log 2) in the calculator will help us find the value of x.

9. Write the equation a ^b = x in log form

Log b (x) = a

Log a (x) = b

Log b (a) = x

Log x (a) = b

The equation a b = x can be rewritten in log form as log a (x) = b. This is because in logarithmic form, the base (a) is raised to the power of the exponent (b) to give the result (x). Therefore, log a (x) = b accurately represents the original equation.

Explanation

The equation a b = x can be rewritten in log form as log a (x) = b. This is because in logarithmic form, the base (a) is raised to the power of the exponent (b) to give the result (x). Therefore, log a (x) = b accurately represents the original equation.

10. Solve the following equation and select one of the answer choices.

30

3

10

Log10

The given equation is asking to solve the logarithmic expression log10(30). The logarithm of a number to the base 10 is the power to which 10 must be raised to obtain that number. In this case, we need to find the power to which 10 must be raised to obtain 30. The answer is 3, as 10^3 equals 1000, which is the closest value to 30.

Explanation

The given equation is asking to solve the logarithmic expression log10(30). The logarithm of a number to the base 10 is the power to which 10 must be raised to obtain that number. In this case, we need to find the power to which 10 must be raised to obtain 30. The answer is 3, as 10^3 equals 1000, which is the closest value to 30.

11.

Solve for x.

3

9

27

1

The answer is 3 because if we look at the pattern of the numbers given (3, 9, 27, 1), we can see that each number is obtained by multiplying the previous number by 3. Therefore, to find the value of x, we need to multiply 1 (the previous number) by 3, which gives us 3.

Explanation

The answer is 3 because if we look at the pattern of the numbers given (3, 9, 27, 1), we can see that each number is obtained by multiplying the previous number by 3. Therefore, to find the value of x, we need to multiply 1 (the previous number) by 3, which gives us 3.

12. Solve

15

125

1.465

0.6826

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Explanation

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13. Condense using log properties then simplify

2

3

4

8

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Explanation

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14. 5^−x = 1/25
Solve for x.

-2

1/2

3

-1

2

Convert the expression to logarithmic form.
5 raised by -2 will get you 1/25.
There is already a negative sign next to the x in the problem, so the answer is 2.

Explanation

Convert the expression to logarithmic form.
5 raised by -2 will get you 1/25.
There is already a negative sign next to the x in the problem, so the answer is 2.