Question 133441
{{{3^(x+2)+3^x = 270}}} Start with the given equation



{{{3^x*3^2+3^x = 270}}} Rewrite {{{3^(x+2)}}} as {{{3^x*3^2}}}



{{{3^x*(3^2+1) = 270}}} Factor out {{{3^x}}}



{{{3^x*(9+1) = 270}}}  Evaluate  {{{3^2}}} to get 9



{{{3^x*(10) = 270}}}  Add



{{{3^x = 27}}}  Divide both sides by 10




{{{log(10,(3^x)) = log(10,(27))}}}  Take the log of both sides



{{{x*log(10,(3)) = log(10,(27))}}}  Rewrite the left side using the identity {{{log(b,(x^y))=y*log(b,(x))}}}



{{{x = log(10,(27))/log(10,(3))}}} Divide both sides by {{{log(10,(3))}}}



{{{x = log(3,(27))}}} Combine the logs



{{{x = 3}}} Evaluate {{{log(3,(27))}}} to get 3




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Answer:


So the answer is {{{x = 3}}}