Question

find the value of x for which 2 raise to x + 4 - 2 raise to x + 2 is equal to 3​

Answer 1

Answer:

${2}^{x + 4} - {2}^{x + 2} = 3 \\ {2}^{x} \times {2}^{4} - {2}^{x} \times {2}^{2} = 3 \\ {2}^{x} \times 16 - {2}^{x} \times 4 = 3 \\ {2}^{x} (16 - 4) = 3 \\ {2}^{x} \times 12 = 3 \\ {2}^{x} = \frac{3}{12} \\ {2}^{x} = \frac{1}{4} \\ {2}^{x} = \frac{1}{ {2}^{2} } \\ {2}^{x} = {2}^{ - 2} \\ x = - 2$