Question 74383
<pre>
Solve the equation:
4^2x+1 = 2^3x+6

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

 2^(4x+2) = 2^(3x+6)    Notice that they have the same base 2
    4x + 2 = 3x + 6     exponent = exponent
    4x - 3x = 6 - 2     Solve or x
          x = 4


Checking:

     4^(((2)(4))+1) = 2^(((3)(4))+6)
                4^9 = 2^18
             262144 = 262144  ----> True