FobelloE

2021-02-09

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

yunitsiL

Skilled2021-02-10Added 108 answers

Given, ${\mathrm{log}}_{2}5$

Change to base 10, we get

$\mathrm{log}}_{2}5=\frac{\mathrm{log}5}{\mathrm{log}2}{:}^{\prime}{\mathrm{log}}_{b}x=\frac{{\mathrm{log}}_{a}x}{{\mathrm{log}}_{a}b$

$=\frac{0.69897}{0.0301029}$

$=2.3219$

Therefore,

${\mathrm{log}}_{2}5=2.3219$

Change to base 10, we get

Therefore,

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