Question

How do I find the logarithm `log_(2/3)(8/27)`?

Answer 1

`color(red)3`

Explanation:

(1)`log_aX^n=nlog_aX`
(2)`log_aa=1`
Now,
`log_(2/3)(8/27)=log_(2/3)(2^3/3^3)=log_(2/3)(2/3)^color(red)(3)` [Applying(1), for n=3]
`=(3)*log_color(red)((2/3))(2/3)=3(1)=3`, [Applying(2) for `a=2/3` ]