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Thread: Logarithm

  1. June 18th 2008, 09:48 AM #1
    cruxkitty
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    Logarithm

    write 1/2log a(x+2) - 3 log a(x-1) + 2 log a x as a single logarithm...
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  2. June 18th 2008, 10:01 AM #2
    Chris L T521
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    Quote Originally Posted by cruxkitty View Post
    write 1/2log 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)

    We know that \log_c a-\log_c b=\log_c\bigg(\frac{a}{b}\bigg), \log_c a+\log_c b=\log_c(ab), and a\log_c b=\log_c(b^a)

    Thus, our expression becomes:

    \log_a(\sqrt{x+2})-\log_a((x-1)^3)+\log_a(x^2) = \log_a\bigg(\frac{\sqrt{x+2}}{(x-1)^3}\bigg)+\log_a(x^2)
    =\color{red}\boxed{\log_a\bigg(\frac{x^2\sqrt{x+2} }{(x-1)^3}\bigg)}

    Hope this makes sense!

    --Chris
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