log

R2026b

Natural logarithm

Syntax

Y = log(X)

Description

Y = log(X) returns the natural logarithm ln(x) of each element in array X.

The log function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally. For negative and complex numbers z = u + i*w, the complex logarithm log(z) returns

log(abs(z)) + 1i*angle(z)

If you want negative and complex numbers to return error messages rather than return complex results, use reallog instead.

Examples

Natural Logarithm of Negative Number

Show that the natural logarithm of -1 is $$i\pi$$.

log(-1)

ans = 
0.0000 + 3.1416i

Input Arguments

X — Input array

scalar | vector | matrix | multidimensional array | table | timetable

Input array, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
Complex Number Support: Yes

Output Arguments

Y — Logarithm values

scalar | vector | matrix | multidimensional array | table | timetable

Logarithm values, returned as a scalar, vector, matrix, multidimensional array, table, or timetable.

For positive real values of X in the interval (0, Inf), Y is in the interval (-Inf,Inf). For complex and negative real values of X, Y is complex. The data type of Y is the same as that of X.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

The log function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• When the input value x is real, but the output should be complex, simulation ends with an error. To produce the complex result, make the input value complex by passing in complex(x).

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• When the input value x is real, but the output should be complex, simulation ends with an error. To produce the complex result, make the input value complex by passing in complex(x).

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

The log function supports HDL code generation with native floating-point for single and double data types. For more information, see Support for Functions in Math Function Block (HDL Coder).

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The log function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The log function supports GPU array input with these usage notes and limitations:

• If the output of the function running on the GPU can be complex, then you must explicitly specify its input arguments as complex. For more information, see Work with Complex Numbers on a GPU (Parallel Computing Toolbox).

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

The log function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2026a: Improved performance in double precision

The log function shows improved performance when computing natural logarithms in double precision. For example, this code computes the natural logarithms of 100,000,000 real numbers within the interval of 0 to 1000. The code is about 2.8x faster than in previous releases.

function t = timingLog
x = rand(1,1e8)*1000;
y = @() log(x);
t = timeit(y);
end

The approximate execution times are:

R2025a: 0.79 s

R2026a: 0.28 s

The code was timed on a Windows^® 11, AMD EPYC™ 74F3 24-Core Processor @ 3.19 GHz test system by calling the timingLog function.

Compatibility Considerations

This performance improvement arises from code changes that also result in slightly different round-off behavior in double precision, leading to more accurate results in general. For example, this code now returns a result that is more accurate to the 15th digit after the decimal point in long scientific notation.

format longE
Y = log(1.63340913276288)

Y =
     4.906693231856701e-01

Previously, the same code returned this result.

format longE
Y = log(1.63340913276288)

Y =
     4.906693231856700e-01

Note that MATLAB^® converts a decimal number input, like 1.63340913276288, to the nearest representable double-precision binary value, which might not be exactly equal to the original decimal input. For this reason, although the log function is now more accurate in double precision, the result might differ from a calculation performed using the exact representation of the input.

R2023a: Perform calculations directly on tables and timetables

The log function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.