The properties of logarithms in this section can be used to rewrite log [ x 4 y 5 √ z ] as follows: A log B + C log D − E log F Find the values below in the same order as the original expression:

Question

A=

B=

C=

D=

E=

F=

Answer 1

log((x^4)(y^5)(sqr(z)))

= log(x^4) + log(y^5) = log(sqr(z))

= 4log(x) + 5log(y) = (1/2)log(z)

A=4, B=y

C=5, D=y

E=-1/2, F = z

UNLESS, the problem was intended to be

log((x^4)(y^5)/z) That seems likely as -ElogF is used rather than +ElogF

IF that's the problem then

log((x^4)(y^5)/z) = 4logx + 5logy -logz

with E=1 instead of -1/2

A still = 4, B=y, C=5, D=y, F=z