Question

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible

$\ln \frac{e^{12}}{8}$

Short answer

The answer is$12-\ln 8$

Step-by-step solution

Step 1. Given

An expression is given as$\ln \frac{e^{12}}{8}$

Step 2. Calculation

If $M>0,N>0,a>0\&a\ne 1$

${\log }_a\frac{M}{N}={\log }_{a}M-{\log }_{a}N$

Use above equation,

$$\begin{gathered} \ln \frac{e^{12}}{8}=\ln e^{12}-\ln 8 \\ =12-\ln 8 \end{gathered}$$