How do you simplify ${log}_{\frac{1}{2}} (\frac{9}{4})$ $log _(1/2) (9/4)$ ?

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Answer 1 · 2016-09-25T05:20:33

$- \frac{ln 9 - ln 4}{ln 2} ≅ - 1.16992$ $-(ln9-ln4)/ln2~=-1.16992$

Remember: ${log}_{a} x = \frac{{log}_{b} x}{{log}_{b} a}$ $log_a x = log_b x/log_b a$

Let $a = \frac{1}{2}, x = \frac{9}{4} and b = e$ $a=1/2, x=9/4 and b=e$

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

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

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

$~= -1.16992$

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