Question

Expand each Logarithm...?
log square root x square root 2 divided by y^2

log base 3 [(xy)1/3]^3

log (xyz)^1/2 divided by z^2

Answer 1

So, in general if you have something like:
\[\ln \left[ \left( \frac{a * b}{c} \right)^{d} \right] = d \ln \left[ \left( \frac{a * b}{c} \right)\right]= d \left[ \ln (a * b) - \ln(c)\right] = d \left[ \ln(a)+\ln(b)-\ln(c)\right]\]
Using these properties:
\[\ln(a*b)=\ln(a)+\ln(b); \ln(a/b)= \ln (a) - \ln(b); \ln(a^b)=b \ln(a)\]
Now try to apply this to your problems. I can help you more if needed.

Answer 2

Could you solve one problem?

Answer 3

\[\ln(\sqrt{2}\sqrt{x}/y^2)=\ln(\sqrt{2x})-\ln(y^2)=\frac{1}{2}\ln(2x)-2\ln(y)=\frac{1}{2}(\ln(2)+\ln(x))-2\ln(y)\]

Answer 4

-2lny** at the end.

Answer 5

why is it so complicated?

Answer 6

Thank you.

Answer 7

No problem.