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

Printable View

- Jun 10th 2011, 07:03 AMPunchinequality
Solve the inequality $\displaystyle -0.02\leqslant -(-\frac{2}{3})^n\leqslant 0.02$

- Jun 10th 2011, 07:24 AMTheEmptySet
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

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

So for $\displaystyle n=10$ the inequality will hold - Jun 10th 2011, 08:21 AMPunch