Question 145339
{{{8^x=100 }}} Start with the given equation.



{{{log(10,(8^x))=log(10,(100)) }}} Take the log base 10 of both sides.



{{{x*log(10,(8))=log(10,(100)) }}} Rewrite the left side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}.



{{{x=log(10,(100))/log(10,(8)) }}} Divide both sides by {{{log(10,(8))}}} to isolate x.



{{{x=log(8,(100))}}} Use the change of base formula to simplify.



So {{{8^x=100 }}} is equivalent to {{{x=log(8,(100))}}}