Use the change-of-base theorem to find an approximation to four decimal places for each logarithm displaystyle{{log}_{{2}}{5}}

FobelloE 2021-02-09 Answered
Use the change-of-base theorem to find an approximation to four decimal places for each logarithm \(\displaystyle{{\log}_{{2}}{5}}\)

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Expert Answer

yunitsiL
Answered 2021-02-10 Author has 12520 answers
Given, \(\displaystyle{{\log}_{{2}}{5}}\)
Change to base 10, we get
\(\displaystyle{{\log}_{{2}}{5}}=\frac{{ \log{{5}}}}{{ \log{{2}}}}:'{{\log}_{{b}}{x}}=\frac{{{{\log}_{{a}}{x}}}}{{{{\log}_{{a}}{b}}}}\)
\(\displaystyle=\frac{0.69897}{{0.0301029}}\)
\(\displaystyle={2.3219}\)
Therefore,
\(\displaystyle{{\log}_{{2}}{5}}={2.3219}\)
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