Question

Expand.

Answer 1

\[\log \sqrt[3]{x*y*z}\]

Answer 2

the idea with these kind of problem is to think in terms of exponents
so the cubed root becomes the exponent of \(\frac{1}{3}\)

Answer 3

\[\log((xyz)^{\frac{1}{3}})\]is the first step

Answer 4

then the one third comes out front as a coefficient

Answer 5

I don't know what to do next.

Answer 6

cube root same as 1/3 so first change that

Answer 7

\[\frac{1}{3}\log(xyz)\]is the next step
then expand the product as a sum

Answer 8

i.e. use the fact that
\[\log(ab)=\log(a)+\log(b)\] make sure to keep that one third out front of the whole thing

Answer 9

Okay so I'll have
\[\frac{ 1 }{ 3 }\log x+ \frac{ 1 }{ 3 } \log y+ \frac{ 1 }{ 3 } \log z\]
Like this?

Answer 10

Or like this?
\[\frac{ 1 }{ 3 } \log x + \log y + \log z\]

Answer 11

remember you have cube root on xyz so all this value have 1/3 power so first one is right

Answer 12

Okay thanks!

Answer 13

\(\color{green}{,my :) pleasure }\)