Question

How do you condense `1/3log_(2)27 - log_(2)9`?

Answer 1

`- log3/log 2=-ln 3/ln 2=-1.585`, nearly.

Explanation:

Use `log_b (m/n)=log_b m - log_b n, nlog_b a =log_b(a^n)` and

`log_b a = log a/log b = ln a/ln b`.

Here, `(1/3)log_2 27-log_2 9=log_2(27^(1/3)) - log_2 9`

`=log_2 3 - log_2 9=log_2(3/9)=log_2(1/3)`

`=-log_2 3=-log 3/log 2=-ln 3/ln 2=-1.585`, nearly