Question

Solve the exponential equation 2^3x-4=2^x+6 by applying the principle that equivalent bases require equivalent exponents. A. 2.5. B. 1. C. 5. D. -5.

Answer 1

Interpret the equation as 2^{3x-4} = 2^{x+6}. Since the bases are equal (2) and 2 ≠ 1, the exponents must be equal:
3x − 4 = x + 6
2x = 10
x = 5.

Check: 2^{3·5−4} = 2^{11} = 2^{5+6}. So the correct choice is C.