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Math Help - Writing an expression as a sum or difference of logs??

  1. #1
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    Writing an expression as a sum or difference of logs??

    Write ln [((x-3)^4(x+5)^1/2)/((2x-7)^9(x^1/3))] as a sum or difference of logarithms with all exponents simplified as far as possible.
    this looks so complicated!! please help?
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  2. #2
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    Quote Originally Posted by yess View Post
    Write ln [((x-3)^4(x+5)^1/2)/((2x-7)^9(x^1/3))] as a sum or difference of logarithms with all exponents simplified as far as possible.
    this looks so complicated!! please help?
    1. Use the following laws of logs:

    \log(a\cdot b)=\log(a)+\log(b)

    \log\left(\dfrac ab \right)=\log(a)-\log(b)

    \log\left(a^n\right)=n\cdot \log(a)

    2. \ln\left(\dfrac{(x-3)^4 \cdot (x+5)^{\frac12}}{(2x-7)^9 \cdot (x)^{\frac13}}  \right) = \ln\left((x-3)^4 \cdot (x+5)^{\frac12}\cdot (2x-7)^{-9} \cdot (x)^{-\frac13}  \right)

    = 4\ln(x-3)+\frac12 \ln(x+5)-9\ln(2x-7)-\frac13 \ln(x)
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  3. #3
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    Quote Originally Posted by earboth View Post
    1. Use the following laws of logs:

    \log(a\cdot b)=\log(a)+\log(b)

    \log\left(\dfrac ab \right)=\log(a)-\log(b)

    \log\left(a^n\right)=n\cdot \log(a)

    2. \ln\left(\dfrac{(x-3)^4 \cdot (x+5)^{\frac12}}{(2x-7)^9 \cdot (x)^{\frac13}}  \right) = \ln\left((x-3)^4 \cdot (x+5)^{\frac12}\cdot (2x-7)^{-9} \cdot (x)^{-\frac13}  \right)

    = 4\ln(x-3)+\frac12 \ln(x+5)-9\ln(2x-7)-\frac13 \ln(x)
    great thank you soo much!
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