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Basic of Logarithms
medium
${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}} = . . . .$
A
$49$
B
$625$
C
$216$
D
$890$
Solution
(d) ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_9}36}} + {3^{4/{{\log }_7}9}}$
$ = {3^{4{{\log }_3}5}} + {3^{3.{1 \over 2}{{\log }_3}36}} + {3^{4{{\log }_9}7}}$
$ = {3^{{{\log }_3}{5^4}}} + {3^{{{\log }_3}{{36}^{3/2}}}} + {3^{{{\log }_3}{7^{4/2}}}}$
$ = {5^4} + {36^{3/2}} + {7^2} = 890$.
Standard 11
Mathematics
