Question

Show that :$\frac{2}{5}<{\log }_{10}3<\frac{1}{2}$.

Answer 1

The statement is true.

$lo{g}_{10}3=log3=0.4774$ or we can use the base change theorem.

$lo{g}_{10}3=\frac{log3}{log10}=log3=0.4774$

$0.4<0.447<0.5$