Question

when you calculate \\( \ln(10) \\), you would be finding the value of which of the following expressions?
\\( 10 \cdot \ln(e) \\)
\\( \log_{e}(10) \\)
\\( \log_{10}(e) \\)
\\( \log(10) \\)

Explanation:

The natural logarithm, denoted as \( \ln(x) \), is a logarithm with base \( e \). By definition, \( \ln(x)=\log_{e}(x) \). So when calculating \( \ln(10) \), it is equivalent to \( \log_{e}(10) \).

• For \( 10\cdot\ln(e) \), since \( \ln(e) = 1 \), this is \( 10\times1=10 \), which is not the same as \( \ln(10) \).
• \( \log_{10}(e) \) is a logarithm with base \( 10 \) (common logarithm) of \( e \), which is different from \( \ln(10) \).
• \( \log(10) \) usually means \( \log_{10}(10)=1 \) (if base - 10 is assumed for the common logarithm), which is not \( \ln(10) \).

Answer:

\(\log_{e}(10)\)