Question

Sendo logba =2 calcule

logab=

log1/a b=​

Answer 1

Explicação passo-a-passo:

Temos que:

$log_{b}(a) = 2$

1)

$log_{a}(b)$

Mudando a base para b:

$log_{a}(b) = \frac{ log_{b}(b) }{ log_{b}(a) }$

Sabemos que:

$log_{b}(b) = 1$

Então:

$log_{a}(b) = \frac{1}{2}$

2)

$log_{ \frac{1}{a} }(b)$

Mudando a base para b:

$log_{ \frac{1}{a} }(b) = \frac{ log_{b}(b) }{ log_{b}( \frac{1}{a} ) }$

$= \frac{1}{ log_{b}(1) - log_{b}(a) }$

Temos que

$log_{b}(1) = 0$

Assim:

$log_{ \frac{1}{a} }(b) = \frac{1}{0 - 2}$

$log_{ \frac{1}{a} }(b) = - \frac{1}{2}$

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