Rewriting Ln function and getting a wrong function?

[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 ?

 

[ShayanJ]

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

 

[christian0710]

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

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?

 

[ShayanJ]

Yes!

 

[HallsofIvy]

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

 

[Ray Vickson]

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 ?

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!