Question

How do you simplify `log _(1/2) (9/4)`?

Answer 1

`-(ln9-ln4)/ln2~=-1.16992`

Explanation:

Remember: `log_a x = log_b x/log_b a`

Let `a=1/2, x=9/4 and b=e`

`:. log_"1/2"(9/4) =ln(9/4)/ln(1/2)`

`= (ln9-ln4)/(ln1-ln2)`

`=(ln9-ln4)/(0-ln2) = - (ln9-ln4)/ln2`

`~= -1.16992`