How to draw a log function?

Question

Ahmad 2016-5-1

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https://ww2.mathworks.cn/matlabcentral/answers/282038-how-to-draw-a-log-function

回答： John BG 2017-2-23

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.

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Answer 1

John BG 2017-2-23

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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:jgb2012@sky.com jgb2012@sky.com>

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Answer 2

John BG 2016-5-2

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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

jgb2012@sky.com

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Ahmad 2016-5-2

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

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Answer 3

Roger Stafford 2016-5-2

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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?

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Ahmad 2016-5-2

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 2016-5-2

编辑：Roger Stafford 2016-5-2

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’.

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