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Math Help - How to simplify this log problem

  1. #1
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    How to simplify this log problem

    I am asked to simply this formula:

    d = ln(45)-ln(35) / ln(81) - ln(49)

    Using the laws of logarithms I am supposed to simplify this expression and show that d = 1/2

    I can see that d = ln(45/35)/ln(81/49) but not sure how that helps.

    Can anyone give me a clue?
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  2. #2
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    Re: How to simplify this log problem

    Quote Originally Posted by angypangy View Post
    I am asked to simply this formula:

    d = ln(45)-ln(35) / ln(81) - ln(49)

    Using the laws of logarithms I am supposed to simplify this expression and show that d = 1/2

    I can see that d = ln(45/35)/ln(81/49) but not sure how that helps.

    Can anyone give me a clue?
    Good start. Now a couple of hints for you:

    \dfrac{45}{35} = \dfrac{5 \times 9}{5 \times 7}

    and

    \dfrac{81}{49} = \left(\dfrac{9}{7}\right)^2

    Does that help?
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  3. #3
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    Re: How to simplify this log problem

    If it were 7/9 / 9^2/7^2 - then it cancels down to 7/9. But this is ln(7/9 / 9^2/7^2) - so can I do it the same way? Does it just become ln(7/9)?
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  4. #4
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    Re: How to simplify this log problem

    \frac{\ln\left(\frac{9}{7}\right)}{\ln\left(\frac{  9}{7}\right)^2} = ?
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