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

1. Solve: ln(4^2x)

   A. 2xln(2) B. 4xln(2) C. log₂4ln² D. ln(2²)

2. Solve: log₄64 = x
   A. 4 B. 3 C. –4 D. 7

Answers and explanations

1. 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:

   

2. 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 log₄(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.