Question

How do you rewrite `log_x(3/10)` as a ratio of common logs and natural logs?

Answer 1

`log(3/10)/logx=-0.5228/logx=-1.204/lnx`

Explanation:

We use the identity `log_ab=logb/loga` (common logs - base `10`) or `lnb/lna` (natural logs).

Hence converting `log_x(3/10)` in common logs, we have

`log(3/10)/logx`

= `(log3-log10)/logx`

= `(log3-1)/log`

= `(0.4771-1)/ogx=-0.5228/logx`

and converting `log_x(3/10)` to natural logs, we have

`ln(3/10)/lnx`

= `(ln0.3)/lnx`

= `-1.204/lnx`