# How do I calculate a logarithm of a variable base?

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Tzahi Shukrun on 2 Oct 2021
Commented: Tzahi Shukrun on 2 Oct 2021
Hi!
I tried to calculate a log of a varying base - no success. I saw that calculating log of the base of 10 or e is possible.
for an example: after typing log (a,b) - I recieve an ERROR message.
I'd like to use "a" as a varying number and change it using a loop until I'll get a good result. "a" can be for an example - 1.05, 1.003....
Here it is:
>> a=1.005;
>> log(a,2)
Error using log
Too many input arguments.
Can you please guide me how doing it?

John D'Errico on 2 Oct 2021
Edited: John D'Errico on 2 Oct 2021
Just write your own function. Save it on your search path. Now you have it.
[log(10),logb(10)] % natural log
ans = 1×2
2.3026 2.3026
[log10(5),logb(5,10)] % log(10) to base 5
ans = 1×2
0.6990 0.6990
[log2(3),logb(3,2)] % log(2) to base 3
ans = 1×2
1.5850 1.5850
logb(16,[2 3 4 5 16]) % log(16) to the bases [2,3,4,5,16]
ans = 1×5
4.0000 2.5237 2.0000 1.7227 1.0000
Simple enough.
function L = logb(X,Base)
% log(X) to the base Base
% If Base is not supplied, then the natural log is presumed.
if (nargin < 2) || isempty(Base)
% default case is the natural log
L = log(X);
else
% test for an invalid base
if any(Base<=0) || any(Base == 1)
error('Base must be > 0, and ~= 1')
end
L = log(X)./log(Base);
end
end

DGM on 2 Oct 2021
Nowhere in the synopsis for log() does it say that it accepts two arguments.
For base 2, you can just use log2()
More generally, just remember the properties of logarithms and use either log(), log10(), or log2() to compute the arbitrary base-n logarithm.

Star Strider on 2 Oct 2021
The general approach is:     So:
a = 64
a = 64
log(a)/log(2)
ans = 6
2^(log(a)/log(2))
ans = 64
See the Wikipedia article on List of logarithmic identities for an extended discussion.
.
Tzahi Shukrun on 2 Oct 2021
First, thank you all for your answers. I wrote it and calculated it that way. Now Im sure that matlab dont have a direct command for this action
Again, thank you very much!

R2018a

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