# How do you solve the exponential inequality 2^(x+3)<=16^(4x-2)?

Feb 17, 2017

$x \ge \frac{11}{15}$

#### Explanation:

Knowing that $16 = {2}^{4}$ we have

${2}^{x + 3} \le {2}^{4 \left(4 x - 2\right)}$

Here $2 > 1$ then if ${2}^{\alpha} \le {2}^{\beta} \to \alpha \le \beta$

so

$x + 3 \le 16 x - 8 \to 15 x \ge 11 \to x \ge \frac{11}{15}$