Question

Expand the following using the properties of logarithms and simplify. Assume when necessary that all quantities represent positive real numbers.

ln((sqaure root of (Z))/(xy))

Answer 1

well start by rewriting the square root in index form

\[\frac{z^{\frac{1}{2}}}{xy}\]

now for division, subtract the logs

\[\ln(\frac{a}{b}) = \ln(a) - \ln(b)\]

the rule for powers is

\[\ln(x^a) = a \times \ln(x)\]

and lastly the rule for multiplication

\[\ln(ab) = \ln(a) + \ln(b)\]

you will use all 3 rules to expand you log expression.

Answer 2

oops it should be

\[\ln(\frac{z^{\frac{1}{2}}}{xy})\]

Answer 3

so this is what i did previously:
(1/2)log(z)-log(x)+log(y)
but apparently it was wrong.That is a math problems website where it tells you if you entered any wrong answers. so the answer I entered was wrong.

Answer 4

nearly... the log(y) is also negative

1/2 log(z) - log(xy) = 1/2 log(z) - (log(x) + log(y))

Answer 5

so you can distribute the negative to get

1/2 log(z) - log(x) - log(y)

Answer 6

i tried that too but it is also wrong and I don't know what is the problem :/

Answer 7

well is it is

\[\log(\sqrt{\frac{z}{xy}})\]

if it is... then its 1/2 of each log...

I worked on

\[\log(\frac{\sqrt z}{xy})\]

which are different expressions.

Answer 8

The expression I gave first which you worked on is the correct one.

Answer 9

ok... there is a floating bracket in the denominator

are you sure its not

\[\frac{\log(\sqrt{z})}{xy}\]

Answer 10

I just got it :3 I kept entering log instead of ln and that was the problem. Thanks for you help any way :)

Answer 11

glad to help