How do you solve log_5(log3x) = 0?

Dec 15, 2015

Use the equivalence:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{{\log}_{b} \left(a\right) = c} \Leftrightarrow \textcolor{b l u e}{{b}^{c} = a}$
to determine
$\textcolor{w h i t e}{\text{XXX}} x = \frac{10}{3}$

Explanation:

${\log}_{5} \left(\log \left(3 x\right)\right) = 0$

$\Rightarrow {5}^{0} = \log \left(3 x\right)$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} \log \left(3 x\right) = 1$

$\log \left(3 x\right) = 1$
$\Rightarrow {10}^{1} = 3 x \textcolor{w h i t e}{\text{XXXXXXXXXXXXX}}$remember the default $\log$ base is $10$
$\rightarrow \textcolor{w h i t e}{\text{XXX}} x = \frac{10}{3}$