How do you solve ${log}_{x} (\frac{1}{256}) = - 4$ $log_x(1/256)=-4$ ?

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Answer 1 · 2018-07-28T08:41:36

The answer is $x = 4$ $x=4$

The equation is

${log}_{x} (\frac{1}{256}) = - 4$ $log_x(1/256)=-4$

By the definition of logs

$x^{- 4} = \frac{1}{256} = \frac{1}{2^{8}} = 2^{- 8}$ $x^(-4)=1/256=1/2^8=2^(-8)$

So,

$\frac{1}{x^{- 4}} = \frac{1}{2^{- 8}}$ $1/x^-4=1/2^-8$

$x^{4} = 2^{8}$ $x^4=2^8$

$x = 2^{\frac{8}{4}} = 2^{2} = 4$ $x=2^(8/4)=2^2=4$

How do you solve logx(1256)=−4log_x(1/256)=-4?