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Math Help - Logarithm

  1. #1
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    Post Logarithm

    Write 1/2 log a (x + 2) - 3 log a (x - 1) + 2 log a X as a single logarithm.
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  2. #2
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    Use the following rules:

    log_{a}x + log_{a}y = log_{a}xy

    log_{a}x - log_{a}y = log_{a}\frac{x}{y}

    \alpha \cdot log_{a}x = log_{a}x^\alpha
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  3. #3
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    Surely you know something about it, otherwise you would not ahve such an assignment. What are your thoughts?

    log(a) + log(b) = log(a*b)

    There are other rules. Use them.
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  4. #4
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    Quote Originally Posted by katchat64 View Post
    Write 1/2 log a (x + 2) - 3 log a (x - 1) + 2 log a X as a single logarithm.
    \frac{1}{2} \log_a(x+2) - 3 \log_a(x-1) + 2 \log_a(x)
    =\log_a(x+2)^\frac{1}{2} - \log_a(x-1)^3 + \log_a(x)^2
    =\log_a \left [ \frac{(x+2)^\frac{1}{2}}{(x-1)^3} \right ] + \log_a(x)^2
    =\log_a \left [ \frac{x^2(x+2)^\frac{1}{2}}{(x-1)^3} \right ]
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