Question

${4}^{2x - 1} - {16}^{x - 1} = 384$
find the value of x​

Answer 1

Answer:

11/4

Step-by-step explanation:

${4}^{2x - 1} - {16}^{x - 1} = 384 \\ {4}^{2x - 1} - {4}^{2(x - 1)} = 384 \\ {4}^{2x - 1} - {4}^{2x - 2} = 384\\ {4}^{2x} \times {4}^{ - 1} - {4}^{2x} \times {4}^{ - 2} = 384 \\ {4}^{2x} ( {4}^{ - 1} - {4}^{ - 2} ) = 384 \\ {4}^{2x} ( \frac{1}{4} - \frac{1}{16} ) = 384 \\ {4}^{2x} \times \frac{3}{16} = 384 \\ {4}^{2x} = 384 \times \frac{16}{3} \\ {4}^{2x} = 128×16 \\ {2}^{2(2x)} = 128×16 \\ {2}^{4x} = {2}^{7} ×{2}^{4} \\ 4x = 11 \\ x = \frac{11}{4}$