# How do you rewrite log_7.1x as a ratio of common logs and natural logs?

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#### Explanation

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#### Explanation:

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1
Alan P. Share
Jan 11, 2017

${\log}_{7.1} x = \textcolor{b l u e}{\frac{{\log}_{10} \left(x\right)}{{\log}_{10} \left(7.1\right)}} = \textcolor{g r e e n}{\frac{\ln \left(x\right)}{\ln \left(7.1\right)}}$

#### Explanation:

The general Change of Base formula is
$\textcolor{w h i t e}{\text{XXX}} {\log}_{b} a = \frac{{\log}_{d} \left(a\right)}{{\log}_{d} \left(b\right)}$

The common log is taken (by most people) to be ${\log}_{10}$
and
the natural log is ${\log}_{e} = \ln$

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