Question

if log b base a = c , then log a base 1/b =. give me a clear process​

Answer 1

Answer:

- c

Step-by-step explanation:

$log_{b}(a) = c \\ \\ log \: formulae \: \\ log_{x}(y) = \frac{1}{ log_{y}(x) } \\ log( \frac{1}{x} ) = - log(x) \\ \\ = > \frac{1}{ log_{a}(b) } = c \\ \\ = > log_{a}(b) = \frac{1}{c} \\ \\ = > - log_{a}(b) = - \frac{1}{c} \\ \\ = > log_{a}( \frac{1}{b} ) = - \frac{1}{c} \\ \\ = > \frac{1}{ log_{a}( \frac{1}{b} ) } = - c \\ \\ = > log_{ \frac{1}{b} }(a) = - c$

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