Question

find the value of my question

Answer 1

$solve : { 5 }^{ log_{ \sqrt{5} }(2) } + {9}^{ log_{3}(7) } - {8}^{ log_{2}(5) } \\ \\ = { \sqrt{5} }^{2 log_{ \sqrt{5} }(2) } + {3}^{2 log_{3}(7) } - {2}^{3 log_{2}(5) } \\ \\ = { \sqrt{5} }^{ log_{ \sqrt{5} }( {2}^{2} ) } + {3}^{ log_{3}( {7}^{2} ) } - {2}^{ log_{2}( {5}^{3} ) } \\ \\ = {2}^{2} + {7}^{2} - {5}^{3} \\ \\ = 4 + 49 - 125 \\ \\ =53 - 125 \\ \\ = -72 \\ \\ note : {x}^{ log_{x}(y) } = y$

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