Question 149962
{{{3(2^x)=42}}} Start with the given equation.



{{{2^x=14}}} Divide both sides by 3.



{{{log(10,(2^x))=log(10,(14))}}} Take the log of both sides.



{{{x*log(10,(2))=log(10,(14))}}} Rewrite the left side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{x=log(10,(14))/log(10,(2))}}} Divide both sides by {{{log(10,(2))}}}.



{{{x=log(2,(14))}}} Use the change of base formula to rewrite the right side.




So the answer is {{{x=log(2,(14))}}} which approximates to {{{x=3.81}}}