Question

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousandth.

Answer 1

Hello,


`log_3(58)= (ln(58))/(ln(3))=3,69597450... \\ log_3(58)=log_4(x)\\ (ln(58))/(ln(3)) = (ln(x))/(4)==\textgreater\ x=e^{ (ln(58)*ln(4))/(ln(3))}\\ =167,957104437222249066099...`

≈167.96

Answer 2

`\log_358\approx 3.696`

`\Rightarrow (\log_458)/(\log_43)`

Explanation:

Given:
`\log_358`

We need to re-write the log expression with base 4 using base change property of log.

Log property:

`\log_ab=(\log_cb)/(\log_ca)`

Evaluate:

`\Rightarrow \log_358`

`\Rightarrow (\log58)/(\log3)`

`\Rightarrow (1.763427)/(0.47712)\approx 3.696`

Convert with base 4:

`\Rightarrow \log_358`

`\Rightarrow (\log_458)/(\log_43)`