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 

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