1. ## A little help with natural logs please?

I have been given this equ ation w = (1/h) ln(L/L0-1) and have been asked to solve for L. I am struggling with when to introduce the 'e'. Can someone please help? Thanks in advance.

2. ## Re: A little help with natural logs please?

Originally Posted by camorris
I have been given this equ ation w = (1/h) ln(L/L0-1) and have been asked to solve for L. I am struggling with when to introduce the 'e'. Can someone please help? Thanks in advance.
\begin{align*}w &= \left( {\frac{1}{h}} \right)\ln \left( {\frac{L}{{{L_0} - 1}}} \right)\\hw&=\ln \left( {\frac{L}{{{L_0} - 1}}} \right)\\e^{hw}&=\frac{L}{L_0-1}\end{align*}

Can you finish?

3. ## Re: A little help with natural logs please?

I think I can

Lo(1_e^hw) ?

Sorry about the notation. I was using my phone.

4. ## Re: A little help with natural logs please?

The point is that "e^x" is the inverse function to "ln(x)". That is, $e^{ln(x)}= x$ and $ln(e^x)= x$. You "introduce the e" (by which I assume you mean "take the exponential of both sides") When you have ln of something on one side and want to get rid of the ln.

(Again, what you wrote, "Lo(1_e^hw)", makes no sense. Did you mean " $(L_0-1)e^{hw}$"?)

5. ## Re: A little help with natural logs please?

Here is the equation I have been asked to solve for L.

I would insert an image but for some reason I am not able to. So I have attached the image to this post. I had an existing equation that I had done before, but I had to work backwards.

I know I went wrong somewhere (You're right, I don't think the 'e' was required).

6. ## Re: A little help with natural logs please?

Originally Posted by camorris
Here is the equation I have been asked to solve for L.

I would insert an image but for some reason I am not able to. So I have attached the image to this post. I had an existing equation that I had done before, but I had to work backwards.

I know I went wrong somewhere (You're right, I don't think the 'e' was required).
Oh...It is 05:30 in the morning here. I cant sleep as I was up half of the night trying to get this done!!! thanks