Thread: Rewriting expression as single log with coefficent 1

I am rewriting the following as a single log with a coefficient of 1:

ln((x^3)-1) - ln((x^2) + x + 1)

Because the coefficient is already zero, I believe I need to divide the two expressions:

ln ( ((x^3)-1) / ((x^2) + x + 1) )

And cancel out the ones...

ln ( (x^3) / ((x^2) + x) )

This seems too easy - can I break it down further?

Originally Posted by Snowcrash

I am rewriting the following as a single log with a coefficient of 1:

ln((x^3)-1) - ln((x^2) + x + 1)

Because the coefficient is already zero, I believe I need to divide the two expressions:

ln ( ((x^3)-1) / ((x^2) + x + 1) )

And cancel out the ones...

ln ( (x^3) / ((x^2) + x) )

You know that cannot be done.
Only factors can be divided out.
But this is true

So this is also true . WHY?