How can I use log form to find the constant k in a given equation?

[phzxc]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[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?

 

[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.

 

[phzxc]

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

 

[Fightfish]

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

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.