Answer
$-\dfrac{3}{2}$
Work Step by Step
RECALL:
(1) $\log_b{M}+\log_b{N}=\log_b{MN}$
(2) $\log_b{M}−\log_b{N}=\log_b{\frac{M}{N}}$
(3) $\log_b{(b^x)}=x$
(4) $\log_b{b}=1$
Write $125$ as $5^3$ to obtain:
$=\log_5{\left(\frac{1}{\sqrt{5^3}}\right)}$
Use the rule "$\sqrt{a^n}=a^{\frac{n}{2}}$" to obtain:
$=\log_5{\left(\dfrac{1}{5^{\frac{3}{2}}}\right)}$
Use the rule "$\dfrac{1}{a^m} = a^{-m}$" to obtain:
$=\log_5{(5^{-\frac{3}{2}})}$
Use rule (3) above to obtain:
$=-\dfrac{3}{2}$
