Answer
Please see the "work step by step" for details.
Work Step by Step
The Quotient Rule states that a logarithm of a QUOTIENT
is a DIFFERENCE of logarithms.
$\displaystyle \log_{\mathrm{b}}(\frac{\mathrm{M}}{\mathrm{N}})=\log_{\mathrm{b}}\mathrm{M}-\log_{\mathrm{b}}\mathrm{N}$
Note the similirity with the Quotient Rule for exponents:
$b^{m}\div b^{n}=b^{m-n}$
(When DIVIDING exponential expressions with the same base,
SUBTRACT the exponents)
-------------
EXAMPLES:
$\displaystyle \log(\frac{z}{100})=\log z-\log 100$
$=\log z-\log 10^{2}=\log z-2$
$\displaystyle \ln(\frac{e^{4}}{x-1})=\ln e^{4}-\ln(x-1)$
$=4-\ln(x-1)$
