Expanding logarithm into sums and differences.

[Belinda]

Please don't be scared when you see this.

The problem asks me to expand the following logarithm into sums and differences of logarithms whose arguments are as simple as possible:

log[((√x²-1)(x²-x)x³)/(x(x-2)10⁴)]

This is what I did:

= log(√x²-1)+log(x²-x)+3log(x)-log(x)+log(x-2)+log(10⁴)

= log(√x²-1)+log(x²-x)+3log(x)-log(x)+log(x-2)+4log(10) as final answer

Not sure if this is correct or if I followed the steps correctly. Would appreciate if someone would look over this and tell me if I did it right.

 

[Deleted member 4993]

Please don't be scared when you see this.

The problem asks me to expand the following logarithm into sums and differences of logarithms whose arguments are as simple as possible:

log[((√x²-1)(x²-x)x³)/(x(x-2)10⁴)]

This is what I did:

= log(√x²-1)+log(x²-x)+3log(x)-log(x) - log(x-2) - log(10⁴)

= log(√x²-1)+log(x²-x)+3log(x)-log(x) - log(x-2) - 4 as final answer

Not sure if this is correct or if I followed the steps correctly. Would appreciate if someone would look over this and tell me if I did it right.

Looks almost good - except the corrections in red.

 

[Belinda]

Looks almost good - except the corrections in red.

Now I am really confused because on another forum I asked the same question and the majority answer was this:

 

[Belinda]

Belinda

You must be very careful with grouping signs. The answer shown above looks like an answer to a problem different from the one you posted on this site.

The question you asked HERE was \(\displaystyle ln\left(\dfrac{(\sqrt{x} - 1)(x^2 - x)x^3}{x(x - 2)10^4}\right)\)

I am guessing that the question you asked there was \(\displaystyle ln\left(\dfrac{\sqrt{x^2 - 1}(x^2 - x)x^3}{x(x - 2)10^4}\right)\)

Yes, the second one. I'm sorry, the square root thing on my Mac doesn't cover the entire expression.

I asked someone else for help and this was their process:

To tell you the truth it confused me a little bit. I'm not sure how he got log(x-2)-4 at the end.

 

[Belinda]

Belinda

You must be very careful with grouping signs. The answer shown above looks like an answer to a problem different from the one you posted on this site.

The question you asked HERE was \(\displaystyle ln\left(\dfrac{(\sqrt{x} - 1)(x^2 - x)x^3}{x(x - 2)10^4}\right)\)

I am guessing that the question you asked there was \(\displaystyle ln\left(\dfrac{\sqrt{x^2 - 1}(x^2 - x)x^3}{x(x - 2)10^4}\right)\)

What is the problem EXACTLY?

It's the second one you stated. I'm sorry, my the square root button on my Mac doesn't cover entire expressions, which is confusing.