${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}} = . . . .$
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d
(d) \({81^{(1/{{\log }_5}3)}} + {27^{{{\log }_9}36}} + {3^{4/{{\log }_7}9}}\)
(d) \({81^{(1/{{\log }_5}3)}} + {27^{{{\log }_9}36}} + {3^{4/{{\log }_7}9}}\)
\( = {3^{4{{\log }_3}5}} + {3^{3.{1 \over 2}{{\log }_3}36}} + {3^{4{{\log }_9}7}}\)
\( = {3^{{{\log }_3}{5^4}}} + {3^{{{\log }_3}{{36}^{3/2}}}} + {3^{{{\log }_3}{7^{4/2}}}}\)
\( = {5^4} + {36^{3/2}} + {7^2} = 890\).
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