Question

Use the change of base theorem to find the logarithm

Answer 1

Step 1

Given;

$log_35$

Required; To simplify using the change of base theorem.

Step 2

State the change of base theorem.

$log_ab=\frac{log_{10}b}{log_{10}a}$

Therefore for the question, we will have;

$log_35=\frac{log_{10}5}{log_{10}3}$

Answer;

$\begin{gathered} \frac{0.6989700043}{0.4771212547}=1.464973521 \\ \approx1.4650 \end{gathered}$

Answer; 1.4650