Solve this equation $3^{(x-3)^{(x+3)}} = (3x+2)^{(x-3)}$ Please can someone help with step by step solving of this equation?
Solve 
$$3^{(x-3)^{(x+3)}} = (3x+2)^{(x-3)},$$
for x
Thanks
A
 A: As Caife answered, $x=3$ is a trivial solution.
However, taking logarithms and graphing the functions $$f(x)=\log \left(3^{(x-3)^{(x+3)}}\right)\qquad \qquad g(x)=\log \left((3 x+2)^{(x-3)}\right)$$ there is another intersection just above $x=4$ but I suspect that only numerical methods will allow you to find its exact value. Using Newton methods (have fun with the derivatives), the solution is almost $x=4.15532$.
Taking into acount the algebra-precalculus tag, I do not suppose that they expect you to find this one. If you are interested in the manner we can get it, just let me know.
A: If you are looking for solutions in the integers, note that $3^{(x-3)^{(x+3)}}$ is a power of $3$, so also $(3x+2)^{(x-3)}$ must be a power of $3$.
On the other hand, $3x+2$ is not divisible by $3$ if $x$ is an integer, so the only possibility is when both sides are $1$. Thus $x=3$ is the only integral solution.
I see no easy algebraic method for determining non integral solutions and I doubt there is one.
A: Try substituting $x=3$. Certainly solves it!
