Question 752775
<pre>
9<sup>x+3</sup> = 3<sup>4x-2</sup>

Write 9 as 3<sup>2</sup>

(3<sup>2</sup>)<sup>x+3</sup> = 3<sup>4x-2</sup>

Multiply the exponent 2 of the base 3 inside the 
parentheses times the exponent x+3.

3<sup>2(x+3)</sup> = 3<sup>4x-2</sup>

Since the bases are the same, 3,  on both sides 
of the equation, the exponents must be equal:

2(x+3) = 4x-2
  2x+6 = 4x-2
   -2x = -8
     x = 4

That's the way you get the answer 4 without
guessing and checking.     

Edwin</pre>