# Property of logarithm

Edit: I answered my own question, I guess this thread serves no purpose so mods, you can delete this.

y = x^2
ln y = ln x^2
ln y = 2 ln x

Can we do the same thing with:

$$y = x^{2/x}$$
$$ln y = ln x^{2/x}$$
$$ln y = \frac{2}{x} x$$

Would that be correct? I just want to make sure because I used this technique for differentiation.

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Doesn't: $$ln y = \frac{2}{x} x$$ just make it 2 :p

But from what I remember about logs, yes you can do that..

gb7nash
Homework Helper
The OP might have already figured this out, but $ln x^{2/x} = \frac{2 ln(x)}{x}$, not $\frac{2}{x}x$. Typo maybe?

The OP might have already figured this out, but $ln x^{2/x} = \frac{2 ln(x)}{x}$, not $\frac{2}{x}x$. Typo maybe?

Yep, it was a typo.