How do you simplify Log_(2)(10)?

Aug 30, 2015

${\log}_{2} \left(10\right) = \frac{1}{\log} \left(2\right)$

Explanation:

Use the change of base formula: ${\log}_{a} \left(b\right) = {\log}_{c} \frac{b}{\log} _ a \left(b\right)$

${\log}_{2} \left(10\right) = {\log}_{10} \frac{10}{\log} _ 10 \left(2\right) = \frac{1}{\log} \left(2\right)$

since ${\log}_{10} = \log$

In general, ${\log}_{a} \left(b\right) = {\log}_{b} \frac{b}{\log} _ b \left(a\right) = \frac{1}{\log} _ b \left(a\right)$