Question

The problem: log(x^(3)y^(2))-2logx√3:(y)-3log((x)/(y))
My answer: log((y^((14)/(3)))/(x^(2)))
Book's answer: log((y^((13)/(3)))/(x^(2)))
What am I doing wrong?

Answer 1

i am a bit confused as to the original problem
it is
\[\log(x^2y^2)-2\log(x\sqrt[3]{y})-3\log(\frac{x}{y})\]?

Answer 2

Almost. The first x^{3}

Answer 3

is not x^{2}

Answer 4

\[\log(x^3y^2)-2\log(x\sqrt[3]{y})-3\log(\frac{x}{y})\]

Answer 5

yes

Answer 6

and you want to combine in to a single log right?

Answer 7

yes

Answer 8

ok then it is mostly bookkeeping with the exponents

Answer 9

\[\log(x^3y^2)-2\log(x\sqrt[3]{y})-3\log(\frac{x}{y})\]
\[\log(x^3y^2)-\log(x^2\sqrt[3]{y^2})-\log(\frac{x^3}{y^3})\]

Answer 10

the input is
\[\frac{x^3y^2y^3}{x^2y^{\frac{2}{3}}x^3}\]

Answer 11

simplifies to
\[\frac{y^{\frac{13}{3}}}{x^2}\]

Answer 12

oh that is what you got!
i think your answer is right

Answer 13

Ok now I see where my mistake was. I didn't distribute the 2 in front of the log, only applied it to the x.

Answer 14

I was off and I couldn't figure it out why. Now i know.

Answer 15

oh that is the book answer
ok i hope it is clear

Answer 16

yes, thank you very much for your help

Answer 17

yw