Question 202841
{{{3^(2x+1)=1/27}}} Start with the given equation.



{{{3^(2x+1)=1/(3^3)}}} Rewrite 27 as {{{3^3}}}



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



{{{2x+1=-3}}} Since the bases are equal, this means that the exponents are equal.



{{{2x=-3-1}}} Subtract {{{1}}} from both sides.



{{{2x=-4}}} Combine like terms on the right side.



{{{x=(-4)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=-2}}} Reduce.



----------------------------------------------------------------------


Answer:


So the solution is {{{x=-2}}}