Question

If 4^x - 4^x-1 = 24.. Find the value of (2x)^x .

Answer 1

${4}^{x} - {4}^{x - 1} = 24 \\ (4 - 1) \times {4}^{x - 1} = 24 \\ 3 \times {4}^{x - 1} = 24 \\ {4}^{x - 1} = 8 \\ {2}^{ 2 \times (x - 1)} = {2}^{3} \\ 2 \times (x - 1) = 3 \\ 2x - 2 = 3 \\ 2x = 5 \\ x = \frac{5}{2}$

Value of x will be $\frac{5}{2}$