# I need help changing an equation

1. Feb 12, 2010

### phzxc

1. The problem statement, all variables and given/known data
So, I'm given the equation T = kL^3/2

Data: L= .9, .8, .7, .6, .5 and T=.558, .47, .375, .323, .26 (.9 goes with .558, etc)

I need to find the constant k by changing T=kL^3/2 into log form

2. Relevant equations

3. The attempt at a solution

Last edited: Feb 12, 2010
2. Feb 12, 2010

### Fightfish

"Rewriting the equation in log form" essentially means to take logarithms on both sides of the equation. So, we obtain
$$log T = log (k\,L^{\frac{3}{2}})$$​

I'm sure you can go on in further simplifying the expression?

3. Feb 12, 2010

### Fightfish

Well, I see you've edited your post with the data.
To solve for k, what we are doing here is actually linearising the relation between T and L so that we can plot a nice straight line.
Simplifying the expression further, we get:
$$log\,T = log\,k + \frac{3}{2}log\,L$$​

Clearly, plotting log T against log L (values obtained from your data) will yield a gradient of 3/2 and a y-intercept of log k. This enables you to obtain the value of k.

4. Feb 12, 2010

### phzxc

how does making the relation linear allow me to find k?

5. Feb 12, 2010

### Fightfish

It allows you to plot a simple straight line graph in the form y = mx + c from which you can extract information from.
As I mentioned in my earlier post, plotting y (log T) against x (log L) will yield a gradient m (3/2) and a y-intercept c (log k). Obtain the y-intercept value from the graph, which is equal to log k, and solve from k from there.