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# log10

Common logarithm (base 10)

## Description

example

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

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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 $1{0}^{1}=10$.

Calculate the common logarithm of 100.

log10(100)
ans = 2

The result is 2 since $1{0}^{2}=100$.

Calculate the common logarithm of 0.

log10(0)
ans = -Inf

The result is -Inf since $1{0}^{-\infty }=0$.

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

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 $lo{g}_{10}\left(X+iY\right)$ 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

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

Data Types: single | double
Complex Number Support: Yes