4.2.2 Change of Base of Logarithms

April 30, 2021July 20, 2013 by

Change of Base of Logarithms

\log_{a} b = \frac{\log_{c} b}{\log_{c} a} and \log_{a} b = \frac{1}{\log_{b} a}

Example:
Find the value of the following:
a.

\log_{25} 100

b.

\log_{3} 0.45

Answer:

\begin{array}{l} (a) \log_{25} 100 = \frac{\log_{10} 100}{\log_{10} 25} = \frac{\log_{10} 10^{2}}{\log_{10} 25} = \frac{2}{1.3979} = 1.431 \\ (b) \log_{3} 0.45 = \frac{\log_{10} 0.45}{\log_{10} 3} = \frac{- 0.3468}{0.4771} = - 0.727 \end{array}

1 thought on “4.2.2 Change of Base of Logarithms”

Adam Lim

March 14, 2019 at 1:23 pm | Reply

a. log 100 should be log 10 to the power of 2, equal 2

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