Logarithms

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ACT Math › Logarithms

Questions 1 - 10
1

If , then ?

4

5

10

15

25

Explanation

Calculate the power of that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:

Solve this equation by taking the square root of both sides.

, because logarithmic equations cannot have a negative base.

The solution to this expression is:

2

If , then ?

4

5

10

15

25

Explanation

Calculate the power of that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:

Solve this equation by taking the square root of both sides.

, because logarithmic equations cannot have a negative base.

The solution to this expression is:

3

Simplify:

Explanation

Here, we need to make use of some logarithm identities:

Therefore, putting all of those things together, we get the final answer of

4

If log4 x = 2, what is the square root of x?

2

3

4

12

16

Explanation

Given log4_x_ = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.

5

Simplify:

Explanation

Here, we need to make use of some logarithm identities:

Therefore, putting all of those things together, we get the final answer of

6

If log4 x = 2, what is the square root of x?

2

3

4

12

16

Explanation

Given log4_x_ = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.

7

How can we simplify this expression below into a single logarithm?

Cannot be simplified into a single logarithm

Explanation

Using the property that , we can simplify the expression to .

Given that and

We can further simplify this equation to

8

How can we simplify this expression below into a single logarithm?

Cannot be simplified into a single logarithm

Explanation

Using the property that , we can simplify the expression to .

Given that and

We can further simplify this equation to

9

Evaluate

log327

9

27

30

3

10

Explanation

You can change the form to

3_x_ = 27

x = 3

10

Evaluate

log327

9

27

30

3

10

Explanation

You can change the form to

3_x_ = 27

x = 3

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