Answer
$x\approx 2.9315$
Work Step by Step
We are asked to solve:
$8^x=444$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation, we get:
$\log_{8}{444}=x$
Next, recall the change of base formula (pg. 464):
$\log_{b}{m}=\frac{\log_{c}{m}}{\log_{c}{b}}$
Applying this property, we get:
$\frac{\log_{10}{444}}{\log_{10}{8}}=x$
$x\approx 2.9315$
We confirm that the answer works:
$8^{2.9315}=444$
$444=444$
