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## Homework Statement

y and x are both close to 1.

[tex]ln(y) - ln(x) \approx (y-x)(lnx)'[/tex]

Can someone explain me why this is true?

By the way, (lnx)' is the derivative of lnx, which is just 1/x

## The Attempt at a Solution

I guess this is something to do with the taylor series of ln(x). I tried to expand ln(y) and ln(x) by taylor series, but I did not get anything from there.

[tex]((y-1)-\frac{(y-1)^{2}}{2}+\frac{(y-1)^{3}}{3}...)-((x-1)-\frac{(x-1)^{2}}{2}+\frac{(x-1)^{3}}{3}...)[/tex]

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