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  4. If 60 a =3 and 60 b =5, then 12((1- a - b )/2(1- b )) is equal to

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Q. If $60^{ a }=3$ and $60^{ b }=5$, then $12^{\frac{(1- a - b )}{2(1- b )}}$ is equal to

Continuity and Differentiability

Solution:

$(60)^a=3 \Rightarrow a=\frac{\log 3}{\log 60} ; (60)^b=5 \Rightarrow b=\frac{\log 5}{\log 60}$
Now, $\frac{1- a - b }{2(1- b )}=\frac{\left(1-\frac{\log 3}{\log 60}-\frac{\log 5}{\log 60}\right)}{2\left(1-\frac{\log 5}{\log 60}\right)}=\frac{(\log 60-\log 15)}{2(\log 60-\log 5)}=\frac{\log 4}{2 \log 12}=\log _{12}(2)$
$\therefore 12^{\frac{(1- a - b )}{2( a - b )}}=12^{\log _{12}(2)}=2 $