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Math Help - exponential equation

  1. #1
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    exponential equation

    8^{X^2 + 1} = 4^{1-x}

    so I did this with a base of 2... do I multiply the first part by 3 or add the 3... and the same on the other side... do I multiply the exponent by 2 or add the 2... I know the answer is \frac{-1}{8} either way I end up with an equation I can't seem to solve.
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  2. #2
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    \displaystyle 8^{x^2 + 1} = 4^{1 - x}

    \displaystyle \left(2^3\right)^{x^2+1} = \left(2^2\right)^{1 - x}

    \displaystyle 2^{3(x^2 + 1)} = 2^{2(1 - x)}

    \displaystyle 3(x^2 + 1) = 2(1 - x).

    Now expand both sides and solve the resulting quadratic.
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