# ASVAB Mathematics Knowledge Practice: Logarithms

When you encounter logarithm problems on the Mathematics Knowledge subtest on the ASVAB, you can use the log rule to solve them. The following practice questions show you how.

## Practice questions

- Solve: ln(4
^{2x})**A.**2*x*ln(2)

**B.**4*x*ln(2)

**C.**log_{2}4ln^{2}

**D.**ln(2^{2}) - Solve: log
_{4}64 =*x*

**A.**4

**B.**3

**C.**–4

**D.**7

## Answers and explanations

- The correct answer is
**Choice (B).**Simplify and apply the log rule that says

Rewrite the 4 in parentheses in power-base form:

Apply the log rule again and multiply the whole numbers:

- The correct answer is
**Choice (B).**Rewrite 64 as a power of 4 and put it in the equation:

Flip the sides of the equation and apply the log power rule, which says

In other words, bring the 3 down and put it in front of the log:

Apply the log rule that says log

(_{a}*a*) = 1 — that is, replace log_{4}(4) with 1:Another approach is to change the log to exponential form:

Rewrite 64 as a power with a base of 4:

The bases are the same, so the exponents must be equal. Therefore,

*x*= 3.