## Calculus with Applications (10th Edition)

$1.5$
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, $\log_{4}8$=$\displaystyle \frac{\ln 8}{\ln 4}=1.5$