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Math Help - Combining log and ln?

  1. #1
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    Combining log and ln?

    I have a problem about condensing logarithmic expressions with logs AND lns. Is this possible?

    ln 5 + 3 ln 3 - log 4
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  2. #2
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    What base are you working in?
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  3. #3
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    That's exactly how the problem appears. I guess just the assumed bases of e and 10.
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  4. #4
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    well log_{e} x = lnx. In that case...

    ln5 + 3ln3 - log4 = ln5 + ln3^3 - ln4
    = ln5 + ln9 - ln4 = ln45 -ln4 = ln \frac{45}{4}

    Hopefully someone will correct me if I'm wrong.
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  5. #5
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    Quote Originally Posted by happydino1 View Post
    I have a problem about condensing logarithmic expressions with logs AND lns. Is this possible?

    ln 5 + 3 ln 3 - log 4
    Why wouldn't this be "possible"?

    ln(5) + 3ln(3) - log(4)

    ln(5*3^3) - log(4)

    ln(135) - log_{10}(4)

    ln(135) - \frac{ln(4)}{ln(10)}

    ln(135) - \frac{ln(4)}{ln(10)}
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  6. #6
    GAMMA Mathematics
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    Quote Originally Posted by WWTL@WHL View Post
    well log_{e} x = lnx. In that case...

    ln5 + 3ln3 - log4 = ln5 + ln3^3 - ln4
    = ln5 + ln9 - ln4 = ln45 -ln4 = ln \frac{45}{4}

    Hopefully someone will correct me if I'm wrong.
    log notation usually means base ten
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  7. #7
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    Quote Originally Posted by colby2152 View Post
    log notation usually means base ten
    My bad.

    I read this on wiki: Mathematicians, statisticians, and some engineers generally understand either "log(x)" or "ln(x)" to mean loge(x) and got confused.

    OP: Ignore my post.
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  8. #8
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    Quote Originally Posted by WWTL@WHL View Post
    I read this on wiki: Mathematicians, statisticians, and some engineers generally understand either "log(x)" or "ln(x)" to mean loge(x) and got confused.
    Of course.

    It's actually applied to integration and derivatives. (As far as I know.)

    There're lots of calculus' books which use that.
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