Loga2=x and loga5=y. Therefore find x and y in a)log₂5 B) loga20?

Answer 1

a)log₂5

=loga 5/loga 2
=y/x


B)
loga20
=loga 2*2*5
=loga 2+loga 2+ loga 5
=x+x+y
=2x+y

Answer 2

log(a) 2 = x -----------------(1)

log(a)5 = y -------------------(2)

A)
log(2) 5

change the base 2 to a

log(2)5 = log(a)5/log(a)2 = y/x

B)

log(a)20 = log(a)(5*4) = log(a)5 + log(a)4

=>log(a)5 + log(a)2^2 = log(a)5 + 2 log(a)2

=>y + 2x