# How do you solve 2^(x+2) - 2^(x+5)= -7?

We have that ${2}^{x + 2} - {2}^{x + 5} = - 7 \implies {2}^{x} \left({2}^{2} - {2}^{5}\right) = - 7 \implies {2}^{x} \cdot \left(- 28\right) = - 7 \implies {2}^{x} = \frac{7}{28} \implies {2}^{x} = \frac{1}{4} \implies {2}^{x} = {2}^{- 2} \implies x = - 2$