# Property of logarithms

posted by
**Jen** on
.

Using property of logarithms, how do I prove derivative of ln(kx) is 1/x

First observe that ln(kx) = ln(k) + ln(x) then take derivatives. The ln(k) is simply a constant so it goes away. You could also derive it as

d/dx ln(kx) = 1/kx * k by the chain rule.

To see that the derivative of ln(x) is 1/x here's a brief proof.

If you have y=ln(x) then

e^{y}=x Now find dx/dy to get

dx/dy = e^{y} because

d/dy e^{y} = e^{y}

So 1/dx/dy = dy/dx = 1/e^{y} = 1/x

This assumes that you know

d/du e^{u} = e^{u} which is easier to derive from the definition than d/dx ln(x).

what are you doing please give alghorthm problums