# Rewriting Ln function and getting a wrong function?

1. Sep 11, 2014

### christian0710

This is really strange: If i rewrite a potens function i get a function which should not be possible (it does not give the same values). What did i do wrong?

Y = b*X^a
lnY = ln(b*X^a)
lny = lnb + ln X^a
lnY = lnb + a*lnx

we raise both sides to e

Y = b+ e^(a*lnx)=b+( e^lnx)^a = b + X^a

I think b+ x^a is very diffrent that b*x^a ????

2. Sep 11, 2014

### ShayanJ

The point is, $e^{x+y}=e^x e^y$ but you assumed $e^{x+y}=e^x+e^y$ which is wrong!

3. Sep 11, 2014

### christian0710

So are you saying that when i raise the right side of an equation (lnb + a*lnx ) to e, I should raise it like this e^(lnb + a*lnx ) and not the individual terms?

4. Sep 11, 2014

### ShayanJ

Yes!

5. Sep 11, 2014

### HallsofIvy

Staff Emeritus
That's exactly what you used when you went from ln(ab) to ln(a)+ ln(b).

6. Sep 11, 2014

### Ray Vickson

You made the same basic error in another thread, and in that thread several people explained to you where your mistake lies. Please pay attention to what people are explaining to you!