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Math Help - inequality

  1. #1
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    inequality

    Solve the inequality -0.02\leqslant -(-\frac{2}{3})^n\leqslant 0.02
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  2. #2
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    Quote Originally Posted by Punch View Post
    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
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    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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