Question

(UFRGS - 2017) Se log5 x = 2 e log10 y = 4, então log20 y/x é:

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_5\:x = 2 \iff x = 5^2 \iff x = 25}$

$\mathsf{log_{10}\:y = 4 \iff y = (10)^4 \iff y = 10.000}$

$\mathsf{log_{20}\:\dfrac{y}{x} = log_{20}\:\dfrac{10.000}{25}}$

$\mathsf{log_{20}\:\dfrac{y}{x} = log_{20}\:400}$

$\mathsf{log_{20}\:\dfrac{y}{x} = log_{20}\:20^2}$

$\boxed{\boxed{\mathsf{log_{20}\:\dfrac{y}{x} = 2}}}$