Question

20)sabendo que
$log_{20}(2) = a$
e
$log_{20}(3) = b$
calculem o valor de
$log_{6}(5) .$
​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_{20}\:2 = a}$

$\mathsf{log_{20}\:3 = b}$

$\mathsf{log_{6}\:5 = \dfrac{log_{20}\:5}{log_{20}\:6}}$

$\mathsf{log_{6}\:5 = \dfrac{log_{20}\:\dfrac{20}{4}}{log_{20}\:(2.3)}}$

$\mathsf{log_{6}\:5 = log_{20}\:20 - 2\:log_{20}\:2 - (log_{20}\:2 + log_{20}\:3)}$

$\mathsf{log_{6}\:5 = 1 - 2a - (a + b)}$

$\boxed{\boxed{\mathsf{log_{6}\:5 = 1 - 3a - b}}}$