ASVAB Mathematics Knowledge Practice: Logarithms

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.