# How do you solve the exponential inequality 8^(2x)>=8^(x+7)?

Feb 19, 2017

$x \ge 7$

#### Explanation:

Note that the function $f \left(x\right) = {8}^{x}$ is a strictly monotonically increasing - and therefore one to one - function from $\left(- \infty , \infty\right)$ to $\left(0 , \infty\right)$.

So:

${8}^{2 x} \ge {8}^{x + 7} \iff 2 x \ge x + 7$

Subtract $x$ from both sides of the simplified inequality to find:

$x \ge 7$