Question

(5^log(25) 9 + 3^log(9) 25)^log(2)5

Answer 1

$(5 ^{log _{25}9 } +3 ^{log _{9}25 } ) ^{log _{2}5 }=(5 ^{log _{5}3 }+ 3^{log _{3} 5}) ^{log _{2}5 }=(3+5) ^{log _{2} 5}=8 ^{log _{8}125 } =$$=125$

Answer 2

Решение:
1) $5^{ log_{25} 9} = 5^{ log_{ 5^{2} } 9} = 5^{ log_{ 5^{2} } 3^{2} } = 5^{ log_{5} 3} = 3$
2) $3^{ log_{ 3^{2} } 5^{2} } = 3^{ log_{ 3 } 5 } = 5$
3) $3 + 5 = 8$
4) $8^{ log_{ 2 } 5} = (2^{ log_{ 2 } 5} )^{3} = 5^{3} = 125$
Ответ: 125.