Answer
$1.5$
Work Step by Step
For $a>0, a\neq 1$, and $x>0,\qquad y=\log_{a}x$ means $a^{y}=x$.
$.................................$
$ \log_{4}8=x$ means $4^{x}=8$,
$4^{x}=8$
$(2^{2})^{x} =2^{3}\qquad \color{blue}{\text{ ...equate the exponents } }$
$2x=3$
$x=\displaystyle \frac{3}{2}=1.5$
With change of base, $\displaystyle \log_{a}x=\frac{\log_{b}x}{\log_{b}a}=\frac{\ln x}{\ln a}$,
using a calculator,
$\log_{4}8$=$\displaystyle \frac{\ln 8}{\ln 4}=1.5$
