# Find L if

1. May 15, 2013

### eddievic

Find L if....

1. The problem statement, all variables and given/known data

$$\omega=\frac{1}{h}In(\frac{L}{Lo}-1)$$

Find L if omega - -2.6, Lo = 16 and h = 1.5
2. Relevant equations

3. The attempt at a solution

-2.6*1.5=In(L/16-1)
-3.9=In(L/16-1
e^-3.9=L/16-1
0.02024=L/16-1
1.02024=L/16
so L=16.32384

2. May 15, 2013

### SteamKing

Staff Emeritus
The correct abbreviation for the natural log is 'lower case L' and 'lower case N'. You have 'Upper case I' and 'lower case N', which is incorrect. Otherwise, your algebra appears to be correct.

3. May 15, 2013

### eddievic

Ok thanks for the help I will use the correct abbreviation in future

4. May 15, 2013

### Staff: Mentor

It's best to substitute the constants at the end of your algebraic manipulation. Doing so sooner can lead to round-off errors.

This is the way I would have done it.
$$\omega=\frac{1}{h}\ln(\frac{L}{L_0}-1)$$
$$\Rightarrow h \omega = \ln(\frac{L}{L_0}-1)$$
$$\Rightarrow e^{h \omega} = \frac{L}{L_0}-1$$
$$\Rightarrow e^{h \omega} + 1 = \frac{L}{L_0}$$
$$\Rightarrow L_0 (e^{h \omega} + 1) = L$$
Now you can replace the constants.

5. May 16, 2013

### eddievic

this makes a lot of sense thanks Mark44