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=(log_(10)b)/(log_(10)a)`

Therefore for the question, we will have;

`log_35=(log_(10)5)/(log_(10)3)`

Answer;

`\begin{gathered} (0.6989700043)/(0.4771212547)=1.464973521 \\ \approx1.4650 \end{gathered}`

Answer; 1.4650