Question

How do you rewrite `log_7.1x` as a ratio of common logs and natural logs?

Answer 1

`log_(7.1)x=color(blue)((log_10 (x))/(log_10 (7.1)))=color(green)((ln(x))/(ln(7.1)))`

Explanation:

The general Change of Base formula is
`color(white)("XXX")log_b a=(log_d(a))/(log_d(b))`

The common log is taken (by most people) to be `log_10`
and
the natural log is `log_e=ln`