Question

Please help: write the expression as a single natural logarithm

Answer 1

`3In3+In9`

This can be further expressed as:

`\begin{gathered} In3^3+In9 \\ \text{Hint: xLoga=Log a}^x \end{gathered}`

This becomes:

`In27+In9`

From the first law of logarithm;

`\text{Loga}+\text{Logb}=\text{Logab}`

Thus, we have:

`\begin{gathered} In27+In9=In(27*9) \\ \Rightarrow In(243) \\ \Rightarrow In3^5=5In3 \end{gathered}`

Hence, the final answer is 5In3