Hello,
I have no clue what property should be used for solving this problem or even how to solve it at all.
Here is the equation:
log_{5}(log_{3}x) = 0
How do I solve this?
$\log_5(\log_3(x))=0$
Use identity,
$\log_ab=\dfrac{\log b}{\log a}$
$\Rightarrow\dfrac{\log\bigg(\dfrac{\log x}{\log(3)}\bigg)}{\log 5}=0$
$\Rightarrow\log\bigg(\dfrac{\log x}{\log(3)}\bigg)=0$
Taking exponent both sides
$\Rightarrow \dfrac{\log x}{\log 3}=1$
$\Rightarrow\log x=\log 3$
$\Rightarrow x=3$
Here is a slightly different way that involves nothing more than $log_a(b) = c \iff b = a^c$ and substitution.
$Find\ x\ given\ log_5(log_3(x)) = 0.$
$Let\ u = log_3(x) \implies$
$log_5(u) = 0 \implies$
$u = 5^0 = 1 \implies$
$1 = u = log_3(x) \implies$
$x = 3^1 = 3.$