Question 460410
{{{3^(x-2) = 81 = 3^4}}}

==> x - 2 = 4 ==> x = 6.

----------------------------------------------------------------------------------
1) You said you can solve for x by trial-and-error, but in fact you have never produced any value for x.  So you still don't know how "to solve" the equation.

2) I don't know what "comprehensive" way you're looking for when what you're doing is basically reducing both terms so that they have the same bases, and then equating powers.  Sorry that didn't seem obvious to you.

3) Just repost the problem so that other tutors can explain to you every word of the solution, as well as show you the "comprehensive" way that's eluded you so far.