Question 176824
{{{27^(4x) = 9^(x+1)}}} Start with the given equation.



{{{(3^3)^(4x) = (3^2)^(x+1)}}} Rewrite 27 as {{{3^3}}}. Rewrite 9 as {{{3^2}}}. 



{{{3^(12x) = 3^(2(x+1))}}} Multiply the exponents.



Since the bases are equal, the exponents are equal.



{{{12x=2(x+1)}}} Set the exponents equal to one another.



{{{12x=2x+2}}} Distribute.



{{{12x-2x=2}}} Subtract {{{2x}}} from both sides.



{{{10x=2}}} Combine like terms on the left side.



{{{x=(2)/(10)}}} Divide both sides by {{{10}}} to isolate {{{x}}}.



{{{x=1/5}}} Reduce.



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


Answer:


So the answer is {{{x=1/5}}}