Answer
$x=3\cdot10^8=300,000,000$
Work Step by Step
Recall the quotient property of logarithms (pg. 462):
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
Applying this property to our equation, we get:
$\log_{10}{\frac{x}{3}}=8$
Next, recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=10, y=8, x=x/3$), we get:
$10^{8}=\frac{x}{3}$
$x=3\cdot 10^8$
$x=300,000,000$
We confirm that the answer works:
$\log (3\cdot 10^8)-\log 3=8$
$\log \frac{3\cdot10^8}{3}=8$
$\log 10^8=8$
$8=8$
