# Use the properties of logarithma to xpand the logarithmic function

## Homework Statement

Use the properties of logarithma to xpand the logarithmic function ln[(x2+1)(x-1)]

## The Attempt at a Solution

[ln x2+ln 1]+[ln x-ln 1]
2 ln x+ln x

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the first step makes sense: $$ln[(x^2+1)(x-1)]=ln(x^2+1)+ln(x-1)$$

but then you continued: $$ln(x^2+1)=ln(x^2)+ln(1)$$

You can't do that, but you can do something else to the $$x^2+1$$...

Mark44
Mentor
the first step makes sense: $$ln[(x^2+1)(x-1)]=ln(x^2+1)+ln(x-1)$$

but then you continued: $$ln(x^2+1)=ln(x^2)+ln(1)$$

You can't do that, but you can do something else to the $$x^2+1$$...
Is the something else you're thinking about factoring x^2 + 1?

I just realized I was stupidly thinking of $$x^2-1$$ not $$x^2+1$$. You can't really factor that term unless you go into imaginary numbers.

Mark44
Mentor
That's what I thought you might be thinking.