Question 113531
{{{log(10,(log(8, (8))))=x}}} Start with the given equation



{{{log(10,(1))=x}}} Evaluate the inner expression {{{log(8,(8))}}} to get 1. Remember {{{log(x,(x))=1}}} for any x.




{{{log(10,(10^0))=x}}} Rewrite {{{1}}} as {{{10^0}}}. This is valid since {{{x^0=1}}} for any x.




{{{0*log(10,(10))=x}}} Now bring out the exponent using the identity {{{log(b,(x^y))=y*log(b,(x))}}}



{{{0*1=x}}} Now evaluate {{{log(10,(10))}}} using the idea that {{{log(x,(x))=1}}}



{{{0=x}}} Multiply



So our answer is {{{x=0}}}