Question

Express ln√ab/c^3 as a sums and difference of logarithms.

Answer 1

First, remember: \[\sqrt{x}=x^{\frac{1}{2}}\]

Then you'll need a few logarithm rules for this:

1.\[\ln x^k=k \cdot \ln x\]
2.\[\ln ab = \ln a + \ln b\]
3.\[\ln \frac{a}{b}= \ln a - \ln b\]

Answer 2

If you carefully apply these rules, you'll get the right answer!

Answer 3

-_-

Answer 4

Why the face? I see nothing wrong with the solution.

Answer 5

Maybe you need a little help with the first step?
Here it is:\[\ln \sqrt{\frac{ ab }{ c^3 }}=\ln \left( \frac{ ab }{ c^3 } \right)^{\frac{ 1 }{ 2 }}=\frac{ 1 }{ 2 }\ln \frac{ ab }{ c^3 }\]
See?
I used my first remark about the square root.
Then I applied Rule #1.

Now you do the next step! It isn't that hard...

Answer 6

= 1/2 in ab/c^3 ? using the power rule?

Answer 7

Yes, I used the power rule to get that.
Now go on with the other rules...

Answer 8

1/2(in ab-in c^3) using the quotient rule?

Answer 9

Yes! BTW replace "in" with "ln" because it's the natural logarithm (ln)

Answer 10

ok

Answer 11

But there is more...

Answer 12

= 1/2 (In a + In b - 3 In c) using the product and power rules?

Answer 13

Right. Well done!

Answer 14

thats it?

Answer 15

Yup, nothing more to be done!