Find ln(x) if log10 x=-3

Jun 2010
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If \(\displaystyle \log_{10} (x) = -3\), what is \(\displaystyle \ln x\)?
 
Last edited by a moderator:
Feb 2010
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\(\displaystyle \ln x = {\log_{10} x\over \log_{10} e}\).
 

Soroban

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Hello, Stud778!

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

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


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

 
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