# Converting equations to linear equations?

Hi, Let's say I have a function f(x) = 2*log(x). I know scientists sometimes plot f(x) on the y axis, but then instead of plotting x on the x-axis they plot log (x) such that the graph becomes linear.

How would i plot a function f(x)= 2*log(x) such that it is linear ?

My attemps - Perhaps i don't understand the logic?
I tried doing this: i set log(x)=t, then i have the equation y=2*t which is linear,

Then i find the values from the equation y=2*t
t y
1 2
2 4
3 6
4 8

Then i plot a graph y on the Y axis and ln(x) on the x axis, but i don't get a linear graph when plotting this :(

I saw from a book that the equation c=constant * T^(1/2) would be plotted as a straight line if you set T^(1/2) =x so you get the graph f(x)=constant*x, and then plot y against T^(1/2) so I was wondering how that worked - the book did not show a working example of how it was plotted.

SteamKing
Staff Emeritus
Homework Helper
Hi, Let's say I have a function f(x) = 2*log(x). I know scientists sometimes plot f(x) on the y axis, but then instead of plotting x on the x-axis they plot log (x) such that the graph becomes linear.

How would i plot a function f(x)= 2*log(x) such that it is linear ?

My attemps - Perhaps i don't understand the logic?
I tried doing this: i set log(x)=t, then i have the equation y=2*t which is linear,

Then i find the values from the equation y=2*t
t y
1 2
2 4
3 6
4 8

Then i plot a graph y on the Y axis and ln(x) on the x axis, but i don't get a linear graph when plotting this :(
You are only going to get a straight line if you plot y vs. t, not y vs. log (x).

But if i plot c vs t^(1/2) in the equation c=2*T^(1/2) then i get a straight line. So is it not possible to do the same with the log function?

And what's the point of graphing a nonlinear equation as a linear graph? I guess it always tells us that a variable is proportional to the y-value?

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