Answer
$\frac{1}{2}\log_5{x}-2$
Work Step by Step
RECALL:
(1) $\log_b{(MN)} = \log_b{M} + \log_b{N}$
(2) $\log_b{(\frac{M}{N})} = \log_b{M} - \log_b{N}$
(3) $\log_b{(b^x)}=x$
(4) $\log_b{(a^n)} = n \cdot \log_b{a}$
(5) $\sqrt{x} = x^{\frac{1}{2}}$
Use rule (2) above to obtain
$=\log_5{(\sqrt{x})}-\log_5{25}
\\=\log_5{(\sqrt{x})}-\log_5{(5^2)}$
Use rule (5) above to obtain:
$=\log_5{(x^{\frac{1}{2}})}-\log_5{(5^2)}$
Use rule (4) above to obtain:
$=\frac{1}{2}\log_5{x}-\log_5{(5^2)}$
Use rule (3) above to obtain:
$=\frac{1}{2}\log_5{x}-2$
