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Math Help - Expand logarithmic expression

  1. #1
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    Expand logarithmic expression

    Use the properties of logarithms to expand this expression:
    log (12x/7)

    Any pointers?
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  2. #2
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    Quote Originally Posted by tsmith View Post
    Use the properties of logarithms to expand this expression:
    log (12x/7)

    Any pointers?
    First use the property log(\frac{a}{b})=log(a)-log(b) to expand:

    log(\frac{12x}{7})=log(12x)-log(7)

    Then use the property log(ab)=log(a)+log(b) to expand the log(12x) term. The final expression is:

    log(12)+log(x) -log(7)

    Edit, yes you can expand log(12) too as eplained in the reply below.
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  3. #3
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    Quote Originally Posted by tsmith View Post
    Use the properties of logarithms to expand this expression:
    log (12x/7)

    Any pointers?
    log_c(ab) = log_c(a) + log_c(b)

    log_c \left(\frac{a}{b}\right) = log_c(a) - log_c(b)

    If you're asked to simplify log(12) [ log(12) = log(4\cdot 3)]you'll need the power law: log_c(a^b) = b\,log_c(a)

    a,b \neq 0 \: ; \: c \neq 0,1



    Spoiler:
    log(12)+log(x)-log(7) = 2log(2)+log(3)+log(x)+log(7)
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