Question

Convert log_{3}45 to natural logarithms then evaluate.

Answer 1

\[\log_{3}45 \]

Answer 2

Use this rule :
\[\log_ab=\frac{\ln b}{\ln a}\]

Answer 3

And you can remark that :
\[45=3^2\times 5\]

Answer 4

ln45/ln3?

Answer 5

@ducksonquack yes :
\[\log_345=\frac{\ln45}{\ln3}=\frac{\ln(3^2\times 5)}{\ln 3}=\cdots\]

Answer 6

so 3.5?

Answer 7

Yes, by using the calculator ;)

Answer 8

Thanks!