Answer
$3$
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:
$=\log_2{(\frac{6}{15})}+\log_2{20}
\\=\log_2{(\frac{2}{5})}+\log_2{20}$
Use rule (1) above to obtain:
$=\log_2{(\frac{2}{5}\cdot 20)}
\\=\log_2{(\frac{40}{5})}
\\=\log_2{8}$
Write $8$ as $2^3$ to obtain:
$=\log_2{(2^3)}$
Use rule (3) above to obtain:
$=3$