Question

How do you rewrite `log_(1/5)x` as a ratio of common logs and natural logs?

Answer 1

`log_b a=log_c a/log_c b`
`log_(1/5) x=log_10 x/log_10 (1/5)`
`log_(1/5) x=ln x/ln (1/5)`

Explanation:

You would apply the formula:

`log_b a=log_c a/log_c b`

Then, for example,

`log_(1/5) x=log_10 x/log_10 (1/5)`

and

`log_(1/5) x=ln x/ln (1/5)`