# How to draw a log function?

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Answered: John BG on 23 Feb 2017
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.

John BG on 23 Feb 2017
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

John BG on 2 May 2016
try this
f = @(x) 1+log10(x)
x=[-20:.1:20]
y=f(x)
plot(x,y)
plot(x,y);grid on
John

#### 1 Comment

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

Roger Stafford on 2 May 2016
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?

Roger Stafford on 2 May 2016
“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.
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 on 2 May 2016
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’.