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

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Answer 1 · 2016-08-31T14:42:01

${log}_{\frac{1}{2}} (\frac{9}{4}) = - 1.17$ $log_(1/2)(9/4)=-1.17$

Let ${log}_{\frac{1}{2}} (\frac{9}{4}) = x$ $log_(1/2)(9/4)=x$ , then

${(\frac{1}{2})}^{x} = \frac{9}{4}$ $(1/2)^x=9/4$ or

$\frac{1}{2^{x}} = \frac{9}{4}$ $1/2^x=9/4$ or

$2^{x} = \frac{4}{9}$ $2^x=4/9$ or

$x = {log}_{2} (\frac{4}{9})$ $x=log_2(4/9)$

= ${log}_{2} 4 - {log}_{2} 9$ $log_2 4-log_2 9$

= $2 - \frac{log 9}{log 2}$ $2-log9/log2$

= $2 - \frac{0.9542}{0.3010}$ $2-0.9542/0.3010$

= $2 - 3.17 = - 1.17$ $2-3.17=-1.17$

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