Question

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

Answer 1

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