The log function does exactly what you want.
log(14 - y)
If you want a base 10 log, you use log10. There is also a log2 function, which gives a base 2 log. Other bases are achieved using the simple relation
log(X)/log(b)
produces a log to the base b. You could write a function for it as:
logb = @(X,b) log(X)/log(b);
logb(9,3)
ans =
2
which is as expected.
Finally, there is the reallog function, which also does the natural log, but it produces an error when the log would have been a complex number.
log(-2)
ans =
0.693147180559945 + 3.14159265358979i
reallog(-2)
Error using reallog
Reallog produced complex result.
But for the more normal case, reallog does the same thing as log.
log(2)
ans =
0.693147180559945
reallog(2)
ans =
0.693147180559945 Answer from John D'Errico on mathworks.com
MathWorks
mathworks.com › matlabcentral › answers › 1465394-how-do-i-calculate-a-logarithm-of-a-variable-base
How do I calculate a logarithm of a variable base? - MATLAB Answers - MATLAB Central
October 2, 2021 - 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.... ... Too many input arguments. ... Sign in to comment. Sign in to answer this question. ... https://www.mathworks.com/matlabcentral/answers/1465394-how-do-i-calculate-a-logarithm-of-a-variable-base#answer_800204
Videos
MathWorks
mathworks.com › symbolic math toolbox › mathematics › mathematical functions
log10 - Log base 10 of symbolic input - MATLAB
This MATLAB function returns the logarithm to the base 10 of x.
MathWorks
mathworks.com › matlabcentral › fileexchange › 14866-logb
logb - File Exchange - MATLAB Central
September 1, 2016 - Examples: 1) To calculate the base 5 logarithm of 3: y = logb(3,5) 2) To calculate element-wise the log of a non-scalar input using different bases: y = logb(magic(3),[1 2 3; 4 5 6; 7 8 9]); See also: log, log10, log2 · Brett Shoelson (2025). logb (https://www.mathworks.com/matlabcentral/fileexchange/14866-logb), MATLAB Central File Exchange.
MathWorks
mathworks.com › symbolic math toolbox › mathematics › mathematical functions
log2 - Base-2 logarithm of symbolic input - MATLAB
For the syntax [F,E] = log2(X), any zeros in X produce F = 0 and E = 0. Input values of Inf, -Inf, or NaN are returned unchanged in F with a corresponding exponent of E = 0. ... Base-2 logarithm values, returned as a symbolic number, vector, matrix, or array of the same size as X.
MathWorks
mathworks.com › matlab › mathematics › elementary math › exponents and logarithms
log10 - Common logarithm (base 10) - MATLAB
Y = log10(X) returns the common logarithm of each element in array X. The function accepts both real and complex inputs. For real values of X in the interval (0, Inf), log10 returns real values in the interval (-Inf ,Inf). For complex and negative real values of X, the log10 function returns ...
MathWorks
mathworks.com › matlab › mathematics › elementary math › exponents and logarithms
log2 - Base 2 logarithm and floating-point number dissection - MATLAB
This MATLAB function computes the base 2 logarithm of the elements of X such that 2Y=X.
EDUCBA
educba.com › home › data science › data science tutorials › matlab tutorial › matlab log
Matlab log | Learn the different examples of Matlab log
March 8, 2023 - This is how our input and output will look like in the Matlab command window: ... As we can see in the output, we have the log of 4 to the base “e” as 1.3863, which is the same as expected by us.
Call +917738666252
Address Unit no. 202, Jay Antariksh Bldg, Makwana Road, Marol, Andheri (East),, 400059, Mumbai
Top answer 1 of 5
17
Consider this example:
%# some random data
x = 2.^(0:10);
y = rand(size(x));
plot(log2(x), y) %# plot on log2 x-scale
set(gca, 'XTickLabel',[]) %# suppress current x-labels
xt = get(gca, 'XTick');
yl = get(gca, 'YLim');
str = cellstr( num2str(xt(:),'2^{%d}') ); %# format x-ticks as 2^{xx}
hTxt = text(xt, yl(ones(size(xt))), str, ... %# create text at same locations
'Interpreter','tex', ... %# specify tex interpreter
'VerticalAlignment','top', ... %# v-align to be underneath
'HorizontalAlignment','center'); %# h-aligh to be centered
2 of 5
15
You can plot directly using the plot command
plot (log2(x), y)
but then your x ticks will be the logarithm rather than the actual value. You could either just change your label
xlabel('Log (base 2) of quantity X');
or you can redo the ticks manually.
xt = get(gca, 'XTick');
set (gca, 'XTickLabel', 2.^xt);
Or you can be really fancy
xticks = 10:25;
set(gca, 'XTick', xticks);
for j = 1:length(xticks)
xtl{j} = ['2^' num2str(xticks(j))];
end
set(gca, 'XTickLabel', xtl)
which will evenly space the tick marks on the log scale, and label them according to their power of 2
MathWorks
mathworks.com › matlabcentral › answers › 1808600-formula-for-changing-the-base-of-a-logarithm-is-loga-n-logb-n-logb-a-a-use-matlab-s-fu
formula for changing the base of a logarithm is: loga(N) = (logb(N))/(logb(a)) (a) Use MATLAB's function log (x) to cal... - MATLAB Answers - MATLAB Central
September 20, 2022 - formula for changing the base of a logarithm is:... Learn more about matlab, log
Quora
quora.com › How-can-I-implement-log-ln-and-e-in-MATLAB
How to implement log, ln, and e in MATLAB - Quora
MATLAB already provides the standard ... environments), here are concise, reliable approaches. ... Natural log: log(x) returns ln(x) (base e)....
MathWorks
mathworks.com › matlabcentral › answers › 52224-log-of-10-base-b-where-b-is-defined-as-1-to-10-in-increments-of-1
Log of 10 base "b" where 'b' is defined as 1 to 10 in increments of 1 - MATLAB Answers - MATLAB Central
October 29, 2012 - It is for school BTW, and all i know is Log(base'b')(X)=log(base'e')(x) over log(base'b'(b) where be is all values between 1-10. Sign in to comment. Sign in to answer this question.
MathWorks
mathworks.com › matlab › mathematics › elementary math › exponents and logarithms
log - Natural logarithm - MATLAB
Y = log(X) returns the natural logarithm ln(x) of each element in array X.
Top answer 1 of 2
1
I think this can answer your question. https://youtu.be/2s3aJfRr9gE?t=284 Claude Shannon was using bits (log base 2) because he was using the uncertainty of a fair coin flip
2 of 2
1
I would wager for the exact same reason we use base 10 for common log, the nonfractional part tells you the length in bits (for base 10 it tells you the number of digits). Not to mention the fact that computers generally do math more native in binary. As is mentioned in the comments, all logarithms are just a constant multiple of each other, so it is really up to taste.
MathWorks
mathworks.com › matlab › mathematics › elementary math
Exponents and Logarithms - MATLAB & Simulink
In addition to common functions like exp and log, MATLAB® has several other related functions to allow flexible numerical calculations. The expm1 and log1p functions compensate for numerical round-off errors in small arguments, while the reallog, realpow, and realsqrt functions restrict the range of these functions to real numbers.
Johns Hopkins University
math.jhu.edu › ~shiffman › 370 › help › techdoc › ref › log10.html
log10 (MATLAB Function Reference)
Description The log10 function operates element-by-element on arrays. Its domain includes complex numbers, which may lead to unexpected results if used unintentionally. Y = log10(X) returns the base 10 logarithm of the elements of X.