Question 140337
{{{3^(-x)=(1/9)^(x+1)}}} Start with the given equation



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



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



{{{1/3^(x)=(1/3^(2(x+1)))}}} Distribute the exponent on the right side



{{{3^(x)=3^(2(x+1))}}} Flip both fractions



Since the bases are equal, this means that the exponents are equal



So {{{x=2(x+1)}}}




{{{x=2x+2}}} Distribute



{{{x-2x=2}}} Subtract 2x from both sides



{{{-x=2}}} Combine like terms on the left side



{{{x=(2)/(-1)}}} Divide both sides by -1 to isolate x




{{{x=-2}}} Divide


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Answer:

So our answer is {{{x=-2}}}