Question

Se log5 x = 2 e Log10 T = 4, então log20 y/x é ?

Answer 1

Acredito que no 2º log seria "y" ao invés de T, certo!?

Sendo assim, temos:

$log_{_5}x~=~2\\\\\\x~=~5^2\\\\\\\boxed{x~=~25}\\\\\\\\log_{_{10}}y~=~4\\\\\\y~=~10^4\\\\\\\boxed{y~=~10000}\\\\\\\\log_{_{20}}\frac{y}{x}~=~A\\\\\\log_{_{20}}\frac{10000}{25}~=~A\\\\\\\frac{10000}{25}~=~20^A\\\\\\400~=~20^A\\\\\\20^2~=~20^A\\\\\\\boxed{A~=~2}$

Resposta:  log[20] (y/x) = 2