Question

find the inverse of the function $f(x)=8^x$.
$g(x)=\square$

Explanation:

Step1: Replace $f(x)$ with $y$

$y = 8^x$

Step2: Swap $x$ and $y$

$x = 8^y$

Step3: Convert to logarithmic form

Recall $a^b=c \iff \log_a c = b$, so:
$\log_8 x = y$

Step4: Replace $y$ with $g(x)$

$g(x) = \log_8 x$
(Alternatively, using change of base formula: $g(x)=\frac{\ln x}{\ln 8}$ or $g(x)=\frac{\log_{10} x}{\log_{10} 8}$ are equivalent)

Answer:

$\log_8 x$ (or equivalent form $\frac{\ln x}{\ln 8}$)