Write the following expression as a sum and/or difference of logarithms. Express powers as factors....

Step 1
We have to expand the logarithmic expression using properties of logarithms:
${\displaystyle \ln \left(\frac{e^4}{8}\right)}$
We know that ${\displaystyle \ln ()}$ is the natural logarithm which has base e.
We know the property of logarithms,
${\displaystyle \log \left(\frac{a}{b}\right)=\log \left(a\right)-\log \left(b\right)}$
${\displaystyle m\log \left(a\right)=\log \left(a^m\right)}$
${\displaystyle {\log }_a\left(a\right)=1}$
Step 2
Applying above properties for the given expression, we get
${\displaystyle \ln \left(\frac{e^4}{8}\right)=\ln \left(e^4\right)-\ln \left(8\right)}$
${\displaystyle =4\ln \left(e\right)-\ln \left(2^3\right)}$
${\displaystyle =4{\log }_e\left(e\right)-\ln \left(2^3\right)}$
${\displaystyle =4\times 1-3\ln \left(2\right)}$
${\displaystyle =4-3\ln \left(2\right)}$
Hence, expanded form of expression is ${\displaystyle =4-3\ln \left(2\right)}$
Note: we can write the value of expanded form of logarithm,
${\displaystyle =4-3\ln \left(2\right)=4-3\times 0.693=1.921}$

Answer is given below (on video)