Answer
Please see the "work step by step" for details.
Work Step by Step
The Product Rule states that a logarithm of a PRODUCT is a SUM of logarithms.
$\log_{\mathrm{b}}(\mathrm{M}\mathrm{N})=\log_{\mathrm{b}}\mathrm{M}+\log_{\mathrm{b}}\mathrm{N}$
Note the similirity with the Product Rule for exponents:
$b^{m}\cdot b^{n}=b^{m+n}$
(When MULTIPLYING exponential expressions with the same base, ADD the exponents)
EXAMPLES:
$\log(10x)=\log(10\cdot x)=\log 10 +\log x=1+\log x$
$\log(300)=\log(100\cdot 3)=\log 100 +\log 3$
$=\log 10^{2}+\log 3=2+\log 3$
$\log(x^{2}-4)=\log[(x+2)\cdot (x-2)]$
$=\log(x+2)+\log(x-2)$
