# How do you solve 3log_3 4a=3?

Jun 9, 2016

${\log}_{3} {\left(4 a\right)}^{3} = 3$

Use the rule $a \log n = \log {n}^{a}$

${\log}_{3} \left(64 {a}^{3}\right) = 3$

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

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

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

$a = \sqrt[3]{\frac{27}{64}}$

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

Hopefully this helps!