Question

Alguém me ajuda, por favor!!

Determine o valor das expressões a seguir:

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Answer 1

$a)\\\\5^{log_{_5}7}~=~x\\\\\\Utilizando~a~propriedade~~b^{log_{_b}a}=a\,,~temos:\\\\\\\boxed{x~=~7}$

$b)\\\\2^{log_{_2}7+log_{_2}3}~=~x\\\\\\Utilizando~a~propriedade~do~logaritmo~do~produto:\\\\\\2^{log_{_2}(7\,.\,3)}~=~x\\\\\\2^{log_{_2}21}~=~x\\\\\\Utilizando~a~propriedade~~b^{log_{_b}a}=a\,,~temos:\\\\\\\boxed{x~=~21}$

$c)\\\\2^{2+2log_{_2}5}~=~x\\\\\\Utilizando~a~propriedade~~log_{_b}b=1\,,~temos:\\\\\\2^{2\,.\,log_{_2}2\,+\,2\,.\,log_{_2}5}~=~x\\\\\\Utilizando~a~propriedade~do~logaritmo~do~expoente:\\\\\\2^{\,log_{_2}2^2~\,+\,log_{_2}5^2}~=~x\\\\\\2^{\,log_{_2}(2^2\,.\,5^2)}~=~x\\\\\\Utilizando~a~propriedade~~b^{log_{_b}a}=a\,,~temos:\\\\\\x~=~2^2\,.\,5^2\\\\\\x~=~4~.~25\\\\\\\boxed{x~=~100}$