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

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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yunitsiL
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,
$$\displaystyle{{\log}_{{2}}{5}}={2.3219}$$