# How do you solve 3^(x-2)>=27?

Nov 5, 2016

#### Answer:

$x \ge \frac{27}{\ln} \left(3\right) + 2$

#### Explanation:

Note that (using an example) $\log \left({x}^{y}\right) = y \log \left(x\right)$

Given$: \text{ } {3}^{x - 2} \ge 27$

Taking logs - You can use any log. I chose natural logs giving:

$\left(x - 2\right) \ln \left(3\right) \ge 27$

$x - 2 \ge \frac{27}{\ln} \left(3\right)$

$x \ge \frac{27}{\ln} \left(3\right) + 2$