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Math Help - Help on This Inequality

  1. #1
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    Help on This Inequality

    i cannot remember how to solve for this:
    9^x^2<=27
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Zamadatix View Post
    i cannot remember how to solve for this:
    9^x^2<=27

    Since the expoential is positive and the log is an increasing function we can take the log of both sides of the equation.

    If you use the base 3 log you get

    \log_3(9)^{x^2}=\log_3(27) \implies 2x^2 \le 3 \iff 2\left(x^2-\frac{3}{2}\right) \le 0

    \left(x-\sqrt{\frac{3}{2}} \right)\left(x+\sqrt{\frac{3}{2}} \right)\le 0 \implies x \in \left[ -\sqrt{\frac{3}{2}},\sqrt{\frac{3}{2}}\right]
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