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Math Help - Logarithm equation

  1. #1
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    Logarithm equation

    Solve \log_{5}(x + 1) + 3\log_{2} 0.5 = \log_{25} (2x)^2
    So these are the steps I have done thus far:
    \log_{5} (x + 1) + \log_{2} \frac{1}{8} = \frac{\log_{5} (2x)^2}{\log_{5} 25}
    \log_{5} (x + 1) + \log_{2} \frac{1}{8} = \frac{1}{2} (\log_{5} (2x)^2)
    \log_{5}(x + 1) + \log_{2} \frac{1}{8} = \log_{5} (2x)
    \log_{2} \frac{1}{8} = \log_{5}(2x^2 + 2x)
    \frac{\log_{5} \frac{1}{8}} {\log_{5} 2} = \log_{5} (2x^2 + 2x)
    \log_{5} \frac{1}{8} = [\log_{5} (2x^2 + 2x)][\log_{5}2]

    I feel as if I'm nowhere close to getting the final answer which is supposed to be x = \frac{1}{249}. Any help and would really be appreciated and thank you in advance.
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  2. #2
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    Notice that 3\log_2(0.5)=-3.
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  3. #3
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    oh!! I can find the answer now
    please forgive my lack of latex:

    Thank you very much for the pointer!
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