Solve without a calculator log_4 (20) - log_4 (45) + log_4 (144)

Log₄20-log₄ 45+log₄144=

log₄ (20/45) + log₄144 = (log_a b - log_a c=log_a (b/c))

log₄[ (20*144) / 45] = (log_a b + log_a c=log_a (b*c))

log₄ (2880/45) =

log₄ (64) = n ⇔ 4^n=64 (log_a x=n ⇔ a^n=x)

4^n=4³ ⇒n=3 (64=4*4*4=4³)

Answer: log₄20-log₄ 45+log₄144=3