# Thread: Taking ln of both sides

1. ## Taking ln of both sides

I need to change y = 1.378x^-.654

and plot it as lny vs lnx

The question says plot the points x=10, 20, 30...100 for the original y=mx+b function. I've done that but I'm not sure how I'd convert it so that it's in the form of lny = lnx + b for the values x=10, 20, 30...100

2. Originally Posted by SportfreundeKeaneKent
I need to change y = 1.378x^-.654

and plot it as lny vs lnx

The question says plot the points x=10, 20, 30...100 for the original y=mx+b function. I've done that but I'm not sure how I'd convert it so that it's in the form of lny = lnx + b for the values x=10, 20, 30...100
Well,
$y = 1.378x^{-0.654}$

$ln(y) = ln \left ( 1.378x^{-0.654} \right )$

$ln(y) = ln(1.378) + ln \left ( x^{0.654} \right )$

$ln(y) = ln(1.378) + 0.654 ln(x)$

$ln(y) = 0.654 ln(x) + ln(1.378)$

So the equation is a line on the log-log plot with a slope of 0.654 and an intercept (where x = 1 not x = 0!) of ln(1.278).

-Dan

3. I’m still having problems with this. I can derive the equation like you have but I’m unsure of how to graph it on excel or something. When I plug in the values of 10,20,30…100 for x, the graph I get is curved. How would I plot it on a log log plot in excel to get a straight line?

4. Originally Posted by SportfreundeKeaneKent
I’m still having problems with this. I can derive the equation like you have but I’m unsure of how to graph it on excel or something. When I plug in the values of 10,20,30…100 for x, the graph I get is curved. How would I plot it on a log log plot in excel to get a straight line?
Write out an Excel spreadsheet like this:
The top columns are going to be x, y, log(x), and log(y). Put your x, y data down the x, y columns, then calculate the log(x) and log(y) for each data point. Now make a graph with log(x) for the x data and log(y) for the y data.

-Dan