## College Algebra (10th Edition)

$\frac{1}{2}$
RECALL: $\sqrt{a} = a^{\frac{1}{2}}, a \ge 0$ Use the rule above to obtain: $\log_{10}{\sqrt{10}}=\log_{10}{(10^{\frac{1}{2}})}$ RECALL: $\log_a{(a^n)} = n, a \gt0, a\ne1$ Using the rule above gives: $\log_{10}{(10^{\frac{1}{2}})}=\frac{1}{2}$ Thus, $\log_{10}{\sqrt{10}}=\frac{1}{2}$