Solve the following exponential equation 22x 2x 1 48 0 Wh

Solve the following exponential equation. 2^2x + 2^x + 1 -48 = 0 What is the exact solution? Select the correct choice below and fill in any answer boxes in your choice. A x = (Type an exact answer, using radicals and log functions as needed.) B. There is no solution.

Solution

2^2x + 2^(x+1) -48 =0

Let 2^x = y

y^2 + 2y -48 =0

y^2 + 8y -6y -48 =0

(y +8)(y -6) =0

y = -8 ; Now 2^x = -8 is not a solution

So, y = 6 ; 2^x = 6

x =ln6/ln2

x = 2.58

x = 2.58