Question 144824
{{{e^x=5}}} Start with the given equation



{{{ln(e^x)=ln(5)}}} Take the natural of both sides



{{{x*ln(e)=ln(5)}}} Rewrite the left side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{x=ln(5)}}} Take the natural log of e to get 1




So our answer is {{{x=ln(5)}}} which is approximately {{{x=1.60944}}}

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{{{e^e^x=2}}} Start with the given equation



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



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



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



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



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



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



So our answer is {{{x=ln(ln(2))}}} which is approximately {{{x=-0.36651}}}