Question 733342
<pre>
32<sup>4x-1</sup> = 16<sup>3x</sup>

32 = 4·8 = (2·2)·(2·4) = (2·2)·(2·2·2) = 2·2·2·2·2 = 2<sup>5</sup>

16 = 4·4 = (2·2)·(2·2) = 2·2·2·2 = 2<sup>4</sup>

So we replace 32 with (2<sup>5</sup>) and 16 with (2<sup>4</sup>):

(2<sup>5</sup>)<sup>4x-1</sup> = (2<sup>4</sup>)<sup>3x</sup>

We remove the parentheses by multiplying the exponents:

2<sup>20x-5</sup> = 2<sup>12x</sup>

Since the bases are the same on both sides, and they are positive and
not equal to 1, we can set the exponents equal to each other:

20x - 5 = 12x
     8x = 5
      x = {{{5/8}}}

Edwin</pre>