# Creating a straight line equation from a logarithm equation?

• April 22nd 2013, 04:58 PM
llama
Creating a straight line equation from a logarithm equation?
Show that the equation relating the magnetic force kx^n to the component of the moveable magnet’s
component of weight along the incline is mg sin θ = kx^n, where m = 0.05 kg is the mass of each
magnet, k is a constant, and g = 9.8 m/s2 is the acceleration due to gravity

Ok so I have a set of values,

sintheta
.05
.1
.15
.2
.25
.30

x(cm)
14.1
9.8
8.2
7
6.4
5.6

The equation that relates them is mgsintheta = kx^n
now I hit both sides with log
log (mgsintheta) = nlog(x) + log(k)

My question is how do I create x and y values that I can plot on a graph. I assume the x(cm) is on my x-axis but I'm confused what goes on my y-axis.

Is it just log(.5) or is it log((9.8*.05*sin(.5)) for the y values?
• April 22nd 2013, 05:14 PM
HallsofIvy
Re: Creating a straight line equation from a logarithm equation?
Quote:

Originally Posted by llama
Show that the equation relating the magnetic force kx^n to the component of the moveable magnet’s
component of weight along the incline is mg sin θ = kx^n, where m = 0.05 kg is the mass of each
magnet, k is a constant, and g = 9.8 m/s2 is the acceleration due to gravity

And what is $\theta$, the angle the incline makes with the horizontal?

Quote:

Ok so I have a set of values,

sintheta
.05
.1
.15
.2
.25
.30

x(cm)
14.1
9.8
8.2
7
6.4
5.6

The equation that relates them is mgsintheta = kx^n
now I hit both sides with log
log (mgsintheta) = nlog(x) + log(k)

My question is how do I create x and y values that I can plot on a graph. I assume the x(cm) is on my x-axis but I'm confused what goes on my y-axis.

Is it just log(.5) or is it log((9.8*.05*sin(.5)) for the y values?
These are values you got from a lab?
You want a linear equation of the form y= Ax+ b so take $y= log(mgsin(\theta)$, $x= log(x)$, NOT x, and $b= log(k)$
• April 22nd 2013, 05:20 PM
llama
Re: Creating a straight line equation from a logarithm equation?
Right Theta is the incline with the horizontal.

Sorry I couldn't quite understand the last thing you wrote. It had a bunch of weird characters my computer didn't feel like loading lol

So I have my y and x axis,

I find out y value from y=log(mgsintheta) and i find my X values from x=log(x) ?

and then my slope is N, and my y-intercept is log(k)?