# How do you solve e^(-2x)<=7?

May 18, 2018

Solution: $x \ge - 0.973 \mathmr{and} x \in \left[- 0.973 , \infty\right)$

#### Explanation:

${e}^{- 2 x} \le 7$ , taking natural log on both sides we get,

$- 2 x \ln \left(e\right) \le \ln \left(7\right) \mathmr{and} - 2 x \le \ln \left(7\right) \left[\ln \left(e\right) = 1\right]$ or

$- 2 x \le \ln \left(7\right) \mathmr{and} - 2 x \le 1.9459$

$- x \le \frac{1.9459}{2} \mathmr{and} - x \le 0.973$ or

$x \ge - 0.973$

Solution: $x \ge - 0.973 \mathmr{and} x \in \left[- 0.973 , \infty\right)$ [Ans]