Question 934781
Your left and right members both are base-ten bases raised to variable powers.  See how both bases are
3 raised to some integer powers.


{{{(3^3)^(4x)=(3^2)^(x+1)}}}


{{{3^(3*4x)=3^(2(x+1))}}}


That is simply both members being base of 3 raised to two different expressions of x.
The bases are equal and because the two members are stated equal, the powers are equal.


{{{3*4x=2(x+1)}}}


{{{12x=2x+2}}}
{{{10x=2}}}
{{{highlight(x=5)}}}