Solve the exponential equation 64x 2 11X 2 Select the cor

Solve the exponential equation. 6^4x - 2 = 11^X + 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. X = (Round to four decimal places as needed. Use a comma to separate answers as needed.) B. There is no solution.

Solution

6 ^(4X-2) = 11 ^(X+2);
TAKE LOGARITHM ON BOTH SIDES WE GET:
(4X-2) log 6 = (X+2) log 11
4x-2 = (x+2) * log 11/log 6
4x-2 = (x+2) * 1.79175;
4x-2 = 1.79175 x + 3.5835;
x(4-1.79175) = 2+3.5835 = 5.5835
2.20825 x = 5.5835
x= 2.52847~= 2.5285

Thus, x~= 2.5285