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#