Question

Your friend claims you can use the change – of – base to write the

expression (In x) as a common logarithm. Is your friend correct?

Explain your reasoning.

Answer 1

We may use the change of base method (https://en.wikipedia.org/wiki/Logarithm#Change_of_base) and write

$\ln x = \log_{e}x = \dfrac{\log_{10}x}{\log_{10}e} = \log_{10}x\cdot \dfrac{1}{\log_{10}e}$ ,

the second multiplier is a constant, so we expressed the natural logarithm as a common logarithm multiplied by a constant.