Question 770900
<pre>

2<sup>6-3x</sup> = 8<sup>x+1</sup>

Since 8 = 2<sup>3</sup> we replace 8 by (2<sup>3</sup>)

2<sup>6-3x</sup> = (2<sup>3</sup>)<sup>x+1</sup> 

We remove the parentheses on the right side by 
multiplying exponents:

2<sup>6-3x</sup> = 2<sup>3x+3</sup>

Since the bases on both sides are the same positive number
other than 1, we may equate the exponents:

6 - 3x = 3x + 3
   -6x = -3
     x = {{{(-3)/(-6)}}}
     x = {{{1/2}}}

Edwin</pre>