ASVAB Mathematics Knowledge Practice: Logarithms - dummies

ASVAB Mathematics Knowledge Practice: Logarithms

By Consumer Dummies

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

    ASVAB_1301

    Rewrite the 4 in parentheses in power-base form:

    ASVAB_1302

    Apply the log rule again and multiply the whole numbers:

    ASVAB_1303

  2. The correct answer is Choice (B).

    Rewrite 64 as a power of 4 and put it in the equation:

    ASVAB_1304

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

    ASVAB_1305

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

    ASVAB_1306

    Apply the log rule that says loga(a) = 1 — that is, replace log4(4) with 1:

    ASVAB_1307

    Another approach is to change the log to exponential form:

    ASVAB_1308

    Rewrite 64 as a power with a base of 4:

    ASVAB_1309

    The bases are the same, so the exponents must be equal. Therefore, x = 3.