How do you solve $log_x(1/256)=-4$ ?

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Answer 1 · 2018-07-28T08:41:36

The answer is $x=4$

The equation is

$log_x(1/256)=-4$

By the definition of logs

$x^(-4)=1/256=1/2^8=2^(-8)$

So,

$1/x^-4=1/2^-8$

$x^4=2^8$

$x=2^(8/4)=2^2=4$

How do you solve log_x(1/256)=-4log_x(1/256)=-4?