How do you solve $3 {log}_{3} 4 a = 3$ $3log_3 4a=3$ ?

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Answer 1 · 2016-06-09T01:05:22

${log}_{3} {(4 a)}^{3} = 3$ $log_3(4a)^3 = 3$

Use the rule $a log n = {log n}^{a}$ $alogn = logn^a$

${log}_{3} (64 a^{3}) = 3$ $log_3(64a^3) = 3$

Recall that if ${log}_{a} (n) = x$ $log_a(n) = x$ , then $a^{x} = n$ $a^x = n$

$64 a^{3} = 27$ $64a^3 = 27$

$a^{3} = \frac{27}{64}$ $a^3 = 27/64$

$a = \sqrt[3]{\frac{27}{64}}$ $a = root(3)(27/64)$

$a = \frac{3}{4}$ $a = 3/4$

Hopefully this helps!

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