Question 199620
{{{3^(x-1)=9^(2x)}}} Start with the given equation.



{{{3^(x-1)=(3^2)^(2x)}}} Rewrite 9 as {{{3^2}}}



{{{3^(x-1)=3^(2(2x))}}} Multiply the exponents



{{{3^(x-1)=3^(4x)}}} Multiply



{{{x-1=4x}}} Since the bases are equal, the exponents are equal.



{{{x=4x+1}}} Add {{{1}}} to both sides.



{{{x-4x=1}}} Subtract {{{4x}}} from both sides.



{{{-3x=1}}} Combine like terms on the left side.



{{{x=(1)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{x}}}.



{{{x=-1/3}}} Reduce.



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Answer:


So the solution is {{{x=-1/3}}} which approximates to {{{x=-0.333}}}.