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Take the x-th root of both sides.

Biology

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Answer

We need to solve the equation 3x=x93^x = x^9.

Step-by-step solution

3 steps

  1. Take the xx-th root of both sides.

    3=(x9)1/x3 = (x^9)^{1/x} 3=x9/x3 = x^{9/x}

  2. Raise both sides to the power of x/9x/9.

    3x/9=(x9/x)x/93^{x/9} = (x^{9/x})^{x/9} 3x/9=x3^{x/9} = x

    So, we are looking for solutions to x=3x/9x = 3^{x/9}.

  3. Test for integer solutions by inspection.

    Let's try x=27x=27.
    Substitute x=27x=27

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