log10

Common logarithm (base 10)

Syntax

Y = log10(X)

Description

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 complex values.

Examples

Calculate Scalar Common Logarithm Values

Examine several values of the base 10 logarithm function.

Calculate the common logarithm of 1.

log10(1)

ans = 
0

The result is 0, so this is the x-intercept of the log10 function.

Calculate the common logarithm of 10.

log10(10)

ans = 
1

The result is 1 since $$10^1=10$$.

Calculate the common logarithm of 100.

log10(100)

ans = 
2

The result is 2 since $$10^2=100$$.

Calculate the common logarithm of 0.

log10(0)

ans = 
-Inf

The result is -Inf since $$10^{-\infty }=0$$.

Real-Valued Common Logarithm

Create a vector of numbers in the interval [0.5 5].

X = (0.5:0.5:5)';

Calculate the common logarithm of X.

Y = log10(X)

Y = 10×1

   -0.3010
         0
    0.1761
    0.3010
    0.3979
    0.4771
    0.5441
    0.6021
    0.6532
    0.6990

Complex-Valued Common Logarithm

Create two Cartesian grids for X and Y.

[X,Y] = meshgrid(0:0.5:1.5,-2:0.5:2);

Calculate the complex base 10 logarithm $$lo{g}_{10}(X+iY)$$ on the grid. Use 1i for improved speed and robustness with complex arithmetic.

Z = log10(X + 1i*Y)

Z = 9×4 complex

   0.3010 - 0.6822i   0.3142 - 0.5758i   0.3495 - 0.4808i   0.3979 - 0.4027i
   0.1761 - 0.6822i   0.1990 - 0.5425i   0.2559 - 0.4268i   0.3266 - 0.3411i
   0.0000 - 0.6822i   0.0485 - 0.4808i   0.1505 - 0.3411i   0.2559 - 0.2554i
  -0.3010 - 0.6822i  -0.1505 - 0.3411i   0.0485 - 0.2014i   0.1990 - 0.1397i
     -Inf + 0.0000i  -0.3010 + 0.0000i   0.0000 + 0.0000i   0.1761 + 0.0000i
  -0.3010 + 0.6822i  -0.1505 + 0.3411i   0.0485 + 0.2014i   0.1990 + 0.1397i
   0.0000 + 0.6822i   0.0485 + 0.4808i   0.1505 + 0.3411i   0.2559 + 0.2554i
   0.1761 + 0.6822i   0.1990 + 0.5425i   0.2559 + 0.4268i   0.3266 + 0.3411i
   0.3010 + 0.6822i   0.3142 + 0.5758i   0.3495 + 0.4808i   0.3979 + 0.4027i

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

Extended Capabilities

Tall Arrays

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

The log10 function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

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

Thread-Based Environment

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

This 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 log10 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™.

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

Version History

Introduced before R2006a

R2023a: Perform calculations directly on tables and timetables

The log10 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.