Question 622899
<pre>            25<sup>2x+3</sup> = 25<sup>5x-9</sup>

Use the principle: The equation B<sup>A</sup> = B<sup>C</sup> is
equivalent to the equation A = C if B > 0 and B &#8800; 1

            25<sup>2x+3</sup> = 25<sup>5x-9</sup>

is equivalent to 

             2x+3 = 5x-9
               12 = 3x
                4 = x 

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

             9<sup>8x-4</sup> = 81<sup>3x+6</sup>

Write 81 as 9<sup>2</sup>

             9<sup>8x-4</sup> = (9<sup>2</sup>)<sup>3x+6</sup>

Multiply exponents on the right to remove the parentheses:

             9<sup>8x-4</sup> = 9<sup>6x+12</sup>

Now we can use the principle: The equation B<sup>A</sup> = B<sup>C</sup> is
equivalent to the equation A = C if B > 0 and B &#8800; 1

             9<sup>8x-4</sup> = 9<sup>6x+12</sup>

is equivalent to 

             8x-4 = 6x+12
               2x = 16
                x = 8

Edwin</pre>