Rewrite using Natural Logarithms Solutions

• To expand and contract natural logarithmic expressions and equations, all terms must be in the      same form    .

• If a natural logarithmic expression contains a number, rewrite it using a    natural logarithm     because $x=\ln \left(e^x\right).$

• Once all terms are written in terms of ln (or as a natural log), expand and contract with the       properties of logs    .

Example 2

Write the equation as a natural log.

Write the equation in exponential form.

Example 3

Write as a single natural logarithm. 

$\frac{1}{2}\ln 35–4$

$$\begin{gathered} \ln \sqrt{35}–\ln e^4 \\ \ln \left(\frac{\sqrt{35}}{e^4}\right) \end{gathered}$$