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Math Help - Having Trouble Solving Logarithmic Equation

  1. #1
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    Having Trouble Solving Logarithmic Equation

    I'm having some trouble with this question. First I have to solve the following equation for x, then I have to substitute the value into g(x) = 5(3x^2)^x. Help would be greatly appreciated!

    Solving For X

    \ln(5x^2) + 6 = 0

    \ln(5x^2) = -6

    e^{\ln(5x^2)} = e^{-6}

     5x^2 = e^{-6}

    x^2 = \frac{e^{-6}}{5}

    \sqrt{x^2} = \frac{\sqrt{e^{-6}}}{\sqrt{5}}

    x = \frac{1}{e^3\sqrt{5}}

    Substitution

    g(x) = 5(3x^2)^x

    g(\frac{1}{e^3\sqrt{5}}) = 5(3x^2)^x

    g(\frac{1}{e^3\sqrt{5}}) = 5(3(\frac{1}{e^3\sqrt{5}})^2)^{\frac{1}{e^3\sqrt{5  }}}

    g(\frac{1}{e^3\sqrt{5}}) = 5((\frac{3}{e^3\sqrt{5}})^2)^{\frac{1}{e^3\sqrt{5}  }}

    g(\frac{1}{e^3\sqrt{5}}) = 5(\frac{9}{(e^3\sqrt{5})^2})^{\frac{1}{e^3\sqrt{5}  }}

    I'm stuck at this point (though I'm not sure if it's correct up to this point either ).

    Thanks in advance!
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Re: Having Trouble Solving Logarithmic Equation

    I agree with your solution for x.

    my evaluation for g(x) = 5(3x^2)^x ...

    g\left(\frac{1}{e^3 \sqrt{5}}\right) = 5\left(\frac{3}{5e^6}\right)^{\frac{1}{e^{3} \sqrt{5}}}
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  3. #3
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    Re: Having Trouble Solving Logarithmic Equation

    Thanks for the reply!

    PEMDAS for the win. xD
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