Question 168767
{{{e^(2x)=8}}} Start with the given equation



{{{ln(e^(2x))=ln(8)}}} Take the natural log of both sides



{{{2x*ln(e)=ln(8)}}}  Rewrite the left side using the identity  {{{ln(x^y)=y*ln(x))}}}. In other words, pull down the exponent and place it in front of the "ln"



{{{2x(1)=ln(8)}}} Take the natural log of "e" to get 1



{{{2x=ln(8)}}} Multiply



{{{x=ln(8)/2}}} Divide both sides by 2 to isolate x



So the answer is {{{x=ln(8)/2}}} which approximates to {{{x=1.03972}}}