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(42x)

    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 loga(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.

About This Article

This article is from the book:

About the book author:

Angie Papple Johnston joined the U.S. Army in 2006 as a Chemical, Biological, Radiological, and Nuclear specialist, ready to tackle chemical weapons in a Level- A HAZMAT suit. She's currently the CBRN noncommissioned officer-in-charge of an aviation battalion in Washington, D.C.

This article can be found in the category: