How Do You Make a Log Base 10 in MATLAB?

To calculate the base 10 logarithm in MATLAB, you use the log10 function.

The base 10 logarithm of a number $x$ is the power to which the number 10 must be raised to get $x$. In MATLAB, calculating this value is straightforward using a built-in function.

Understanding the log10 Function

The primary function for computing the common logarithm (log base 10) in MATLAB is log10. This function operates element-wise on arrays, meaning it calculates the base 10 logarithm for each element in the input array.

Based on the provided reference:

• The syntax is Y = log10( X ).
• X is the input array containing the numbers for which you want to find the log base 10.
• Y is the output array containing the base 10 logarithms of the elements in X.

Input and Output Behavior:

• For real values of X in the interval (0, Inf), the log10 function returns real values in the interval (-Inf, Inf).
• For complex and negative real values of X, the log10 function returns complex values.
• The function accepts both real and complex inputs.

How to Use log10 in MATLAB

Using the log10 function is simple. You just pass the number or array you want to operate on as the argument to the function.

Examples:

Let's look at some practical examples.

• Calculating the log base 10 of a single number:

% Calculate log10 of 100
result = log10(100);
disp(result);
% Expected output: 2

% Calculate log10 of 0.1
result = log10(0.1);
disp(result);
% Expected output: -1

• Calculating the log base 10 of an array:

% Create an array of numbers
data = [10, 100, 1000, 0.01, 1];

% Calculate log10 for each element
log_data = log10(data);
disp(log_data);
% Expected output: [1, 2, 3, -2, 0]

• Handling negative or complex inputs (as per reference):

% Calculate log10 of a negative real number
neg_input = -10;
log_neg = log10(neg_input);
disp(log_neg);
% Expected output: a complex number (e.g., 1 + 1.36449j)

% Calculate log10 of a complex number
complex_input = 1 + 1i;
log_complex = log10(complex_input);
disp(log_complex);
% Expected output: a complex number (e.g., 0.1505 + 0.1956j)

Related Logarithm Functions in MATLAB

While log10 is specifically for base 10, MATLAB also provides functions for other common logarithm bases:

You can calculate a logarithm for any arbitrary base b using the change of base formula: $\log_b(x) = \frac{\log_c(x)}{\log_c(b)}$, where c is any base (commonly e or 10). In MATLAB, this would typically be done using log or log10. For example, $\log_5(125)$ could be calculated as log10(125) / log10(5) or log(125) / log(5).

Using log10(X) is the most direct and standard way to compute the base 10 logarithm in MATLAB.