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:

$\begin{gathered} In27+In9=In(27\times9) \\ \Rightarrow In(243) \\ \Rightarrow In3^5=5In3 \end{gathered}$

Hence, the final answer is 5In3