Answer
$-2$
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) $\log_b{b}=1$
Use rule (2) above to obtain:
$=\log_3{(\frac{100}{18})}-\log_3{50}
\\=\log_3{(\frac{50}{9})}-\log_3{50}$
Use rule (2) above to obtain:
$=\log_3{\left(\dfrac{\frac{50}{9}}{50}\right)}
\\=\log_3{\left(\frac{50}{9(50)}\right)}$
Cancel the common factor $50$ to obtain:
$=\log_3{(\frac{1}{9})}$
Write $9$ as $3^2$ to obtain:
$=\log_3{(\frac{1}{3^2})}$
Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain:
$=\log_3{(3^{-2})}$
Use rule (3) above to obtain:
$=-2$
