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Hard Logarithm Question

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(\log_3 p)^2 = \log_3(p^2)
    

\log_3(p+q)=\log_3 p + \log_3 q

    Solve these simultaneous equations.

    I've got  (\log_3 p)^2 = \log_3 (\frac{p^2 +qp}{q}) so far, but I don't know how to eliminate q.
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    Solving the first equation gives you p, and then it's easy to find q from the 2nd.
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    Ok thanks, got it.
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    (Original post by Dan12)
    How do you find p?
    In the first equation, for the RHS, use the logarithmic identity that states that "the logarithm of the n-th power of a number is the same as n times the logarithm of the number." Then, treat the entire equation as a quadratic in log_3p (hint: substitute m=log_3p). Let me know if you still don't get it.
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    Q1. (log3P)2 = log3(P2)
    (log3P)2 = 2(log3P)

    Let log3P = x

    x2 = 2x
    x = 2

    log3P = 2
    P = 9

    Q2. log3(P+Q) = log3P + log3Q
    log3(P+Q) = log3(PQ)
    P+Q = PQ

    Substitute P = 9 from Q1

    9+Q = 9Q
    9 = 8Q
    9/8 = Q
    Q= 1 1/8 or 1.125


    Therefore, P is 9 and Q is 1.25
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    (Original post by 2012_jonathan_s)
    ...
    Welcome to TSR Jonathan.

    Two rules you should know.

    Don't bump old threads for no reason.

    Don't provide full solutions.

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