Answer
$x\approx3.4650$
Work Step by Step
isolate $3^x$ on one side:
$-3^x=-40-5$
$-3^x=-45$
$3^x=45$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=3, y=x, x=45$), we get:
$\log_{3}{45}=x$
Next, recall the change of base formula (pg. 464):
$\log_{b}{m}=\dfrac{\log_{c}{m}}{\log_{c}{b}}$
Applying this formula to our last equation, we get:
$\log_{3}{45}=x$
$\dfrac{\log_{10}{45}}{\log_{10}{3}}=x$
$x\approx3.4650$
