inequality

**Punch** · June 10th 2011, 07:03 AM

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

**TheEmptySet** · June 10th 2011, 07:24 AM

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

**Punch** · June 10th 2011, 08:21 AM

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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