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Math Help - Finding the real solutions of a logarithm

  1. #1
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    Finding the real solutions of a logarithm

    Hi guys,

    What are the real solutions, in any, of log(x) = 2log(3) + log(5) - log(2) - 1
    (all logs are to base 10)

    Thanks in advance for help.
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  2. #2
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    Re: Finding the real solutions of a logarithm

    Quote Originally Posted by Coshy View Post
    Hi guys,

    What are the real solutions, in any, of log(x) = 2log(3) + log(5) - log(2) - 1
    (all logs are to base 10)

    Thanks in advance for help.
    \begin{aligned} \log(x) &= 2\log(3) + \log(5) - \log(2) -1  \\ &= \log(3^2) + \log(5) -\log(2) -1 \\ &= \log( (3^3\times 5)/(2 \times b)) \end{aligned}

    where b is the base for the logarithms, so x= ...

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  3. #3
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    Re: Finding the real solutions of a logarithm

    IF you know the "laws of logarithms": a log(b)= log(b^a) and log(a)+ log(b)= log(ab), this problem is easy. If you do NOT the you should not be attempting a problem like this.
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  4. #4
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    Re: Finding the real solutions of a logarithm

    Finding the real solutions of a logarithm-09-aug-13.png
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  5. #5
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    Re: Finding the real solutions of a logarithm

    Quote Originally Posted by ibdutt View Post
    Click image for larger version. 

Name:	09 Aug 13.png 
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    You are assuming that an unqualified \log denotes \log_{10} which might be the case in high school maths classes but is not in the wider world.

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  6. #6
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    Re: Finding the real solutions of a logarithm

    Quote Originally Posted by Coshy View Post
    What are the real solutions, in any, of log(x) = 2log(3) + log(5) - log(2) - 1
    (all logs are to base 10)
    Quote Originally Posted by zzephod View Post
    You are assuming that an unqualified \log denotes \log_{10} which might be the case in high school maths classes but is not in the wider world..
    The OP clearly states they are indeed base 10.
    Please read the entire thread before positing.
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  7. #7
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    Re: Finding the real solutions of a logarithm

    ..
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