Question 144391
{{{a^x=b}}} Start with the given equation



{{{log(10,(a^x))=log(10,(b))}}} Take the log of both sides




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



{{{x=log(10,(b))/log(10,(a))}}} Divide both sides by {{{log(10,(a))}}}



{{{x=log(a,(b))}}} Simplify the right side by use of the change of base formula.