Question 64217
<pre><font face = "arial" size = 6 color = "darkblue"><b>
     4<sup>2x+1</sup> = 2<sup>3x+6</sup>

Rewrite 4 as (2<sup>2</sup>)

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

Remove the parentheses on the left by
multiplying the inner exponent 2 by
the outer exponent 2x+1

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

Now use the rule which says

<font color = "red"><i>if A<sup>B</sup> = A<sup>C</sup> with A > 0 and A <font face = "symbol">¹</font> 1,

    then B = C</i></font>

So we have:

  2(2x + 1) = 3x + 6

Can you solve that? If not post again,
but I think you can.

Answer: x = 4

Edwin</pre>