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Thread: Find ln(x) if log10 x=-3

  1. June 8th 2010, 12:04 PM #1
    Stud778
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    Find ln(x) if log10 x=-3

    If \log_{10} (x) = -3, what is \ln x?
    Last edited by mr fantastic; June 9th 2010 at 12:35 AM. Reason: Re-titled, added latex tags.
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  2. June 8th 2010, 12:06 PM #2
    maddas
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    \ln x = {\log_{10} x\over \log_{10} e}.
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  3. June 8th 2010, 12:19 PM #3
    Soroban
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    Hello, Stud778!

    \text{If }\log_{10} x\:=\:-3,\,\text{ find }\ln x.

    We have: . \log_{10}x = -3 \quad\Rightarrow\quad x \:=\:10^{-3}


    Then: . \ln x \;=\;\ln\left(10^{-3}\right) \;=\;-3\ln10
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