How to draw a log function?

I love function handles in matlab, I can do this for example:

f = @(x,a,b) a*(x.^b);
plot(x,f(x,a,b));

This is so useful! I want to be able to plot log(y)=1+log(x), I tried:

f = @(x) 1+log10(x);
plot(x,f(log10(f(x));

It doesn't however give a straight line, so this syntax might be wrong! Please tell me how I can do it. Thanks.

Answer 1

[John BG]

is this what you are after?

clc
close all
warning off
z = @(x) 10.^(-.3+(1.75*log10(x)));
y = @(x) (10.^-.3)*(x.^1.75);
x = -100:0.5:100;
plot(x,z(x),'-b','LineWidth',2)
grid on
figure
loglog(x,y(x),'-r','LineWidth',2)
grid on

.

John BG

<mailto:[e-mail] [e-mail]>

Answer 2

[John BG]

Ahmad

try this

f = @(x) 1+log10(x)
x=[-20:.1:20]
y=f(x)
plot(x,y)
plot(x,y);grid on

If you find this answer of any help solving your question,

please click on the thumbs-up vote link,

thanks in advance

John

[e-mail]

[Ahmad]

i appreciate ur help, but plz read my question again, i wanna plot logy=1+logx which should give a straight line

Answer 3

[Roger Stafford]

The quantity f(log10(f(x)) does not yield the solution to log10(y) = 1 + log10(x). It is actually equal to

   f(log10(f(x)) = f(log10(1+log10(x))) = 1+log10(log10(1+log10(x)))

If you were to take the log10 of that, you certainly would not come back to 1+log10(x).

To solve for y, take 10 to the power of both sides of the equation

   y = 10^(log10(y)) = 10^(1+log10(x)) = (10^1)*(10^log10(x)) = 10*x

What could be simpler?

[John BG]

correct, don't expect a straight line unless you take power 10^ to 'bend back up' the log

[Ahmad]

Not correct, I'm afraid, I tried this, however obviously z and y are identical and nonlinear!

clc
close all
warning off
z = @(x) 10.^(-.3+(1.75*log10(x)));
y = @(x) (10.^-.3)*(x.^1.75);
x = -100:0.5:100;
plot(x,z(x),'-b','LineWidth',2)
grid on
figure
plot(x,y(x),'-r','LineWidth',2)
grid on

Again, I'm trying to do this in matlab, help!

[Roger Stafford]

“Not correct, I'm afraid, I tried this, however obviously z and y are identical and nonlinear!”

Hey, no fair, Ahmad! You slipped in a factor of 1.75 on your trial. You have 10.^(-.3+1.75*log10(x)) instead of your original 1+log10(x). Naturally you won’t get a straight line with that. The -.3 doesn’t make it nonlinear, but the 1.75 does.

In any case you now know how to plot log10(y) = -.3+1.75*log(x). Just take ten to the power of each side of the equation. Of course, it won't be linear with the 1.75 factor present.

[Ahmad]

lol sorry i gave a simple example, but honestly are u telling me i can't plot that equation and get the same graph shown in matlab?

[Roger Stafford]

The plot you show in your previous comment plots log(y) against log(x) or log10(y) against log10(x), I’m not sure which. With the equation log(y) = -.3+1.75*log(x) you will naturally get a straight line with this kind of plot. However, that is not the same thing as plotting y against x. For the equation log(y) = -.3+1.75*log(x) you will NOT get a straight line with y against x. For the equation log(y) = 1 + log(x), or log10’s either one, you WILL get a straight line with y against x. The present or absence of the factor 1.75 makes the difference.

Incidentally you should be careful to distinguish between logarithms base ten and natural logarithms with a base e. In matlab the natural logarithm is indicated by ‘log’ whereas logarithm base ten is indicated by ‘log10’.