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Math Help - Logarithm Problem URGENT!!!

  1. #1
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    Logarithm Problem URGENT!!!

    I have had a problem with logarithm problems and one in particular; the problem states: log 5^x+1= log 3^x. Can you please help me with this problem and explain the steps as well? Thank you.
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  2. #2
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    Quote Originally Posted by aussiekid90
    I have had a problem with logarithm problems and one in particular; the problem states: log 5^x+1= log 3^x. Can you please help me with this problem and explain the steps as well? Thank you.
    \log 5^x+1=\log 3^x, by the exponent rule for logarithms you may "bring down" the x thus,
    x\log 5+1=x\log 3
    Then,
    x\log 5-x\log 3=-1
    Thus,
    x(\log 5-\log 3)=-1
    Thus,
    x=-\frac{1}{\log 5-\log 3}=\frac{1}{\log 3-\log 5}
    Q.E.D.
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  3. #3
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    Sorry, typo, the problem would actually be 5^(x+1)=3^x
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  4. #4
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    Quote Originally Posted by aussiekid90
    Sorry, typo, the problem would actually be 5^(x+1)=3^x
    Take the logarithm of both sides,
    \log 5^{x+1}=\log 3^x
    Now use the exponent rule and "bring down" exponents,
    (x+1)\log 5=x\log 3
    Open parantheses,
    x\log 5+\log 5=x\log 3
    Rearrange,
    x\log 5-x\log 3=-\log 5
    Factor,
    x(\log 5-\log 3)=-\log 5
    Thus,
    x=-\frac{\log 5}{\log 5-\log 3}\approx -3.15
    Q.E.D.
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