# Thread:

1. ## inequality

Solve the inequality $-0.02\leqslant -(-\frac{2}{3})^n\leqslant 0.02$

2. Originally Posted by Punch
Solve the inequality $-0.02\leqslant -(-\frac{2}{3})^n\leqslant 0.02$
I am going to assume that n is an integer otherwise the power may give complex values and they are not ordered.

To get a ruff Idea of the bound solve

$\left(\frac{2}{3} \right)^n=0.02 \iff n=\frac{\ln(0.02)}{\ln\left( \frac{2}{3}\right)} \approx 9.68...$

So for $n=10$ the inequality will hold

3. Originally Posted by TheEmptySet
I am going to assume that n is an integer otherwise the power may give complex values and they are not ordered.

To get a ruff Idea of the bound solve

$\left(\frac{2}{3} \right)^n=0.02 \iff n=\frac{\ln(0.02)}{\ln\left( \frac{2}{3}\right)} \approx 9.68...$

So for $n=10$ the inequality will hold
sorry but i dont understand the rationale behind the workings
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