gives the base-10 logarithm of x.


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Log10 gives exact rational number results when possible.
  • For certain special arguments, Log10 automatically evaluates to exact values.
  • Log10 can be evaluated to arbitrary numerical precision.
  • Log10 automatically threads over lists.


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Basic Examples  (5)

Log10 gives the logarithm to base 10:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Series expansion shifted from the origin:

Asymptotic expansion at a singular point:

Scope  (42)

Numerical Evaluation  (6)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number inputs:

Evaluate efficiently at high precision:

Log10 can deal with realvalued intervals:

Log10 threads elementwise over lists and matrices:

Specific Values  (5)

Values of Log10 at fixed points:

Values at infinity:

Zero argument gives a symbolic result:

Zero of Log10:

Find a value of x for which the Log10[x]=0.5 using Solve:

Visualization  (3)

Plot the Log10 function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

Function Properties  (10)

Log10 is defined for all positive values:

Log10 is defined for all nonzero complex values:

Log10 achieves all real values:

The range for complex values:

Log10 is not an analytic function:

Nor is it meromorphic:

Log10 has a branch cut along the negative real axis:

Log10 is monotonic on the positive reals:

Log10 is injective:

Log10 is surjective:

Log10 is neither non-negative nor non-positive:

Log10 has both singularities and discontinuities for x0:

Log10 is concave on the positive reals:

TraditionalForm formatting:

Differentiation  (3)

First derivative:

Higher derivatives:

Plot the higher derivatives:

Formula for the ^(th) derivative:

Integration  (4)

Compute the indefinite integral using Integrate:

Definite integral:

Definite integral of Log10:

More integrals:

Series Expansions  (5)

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:


Log10 can be applied to power series:

Asymptotic expansions at the branch cut:

Function Identities and Simplifications  (6)

Basic identity for Log10:

Logarithm of a power function simplification:

Simplify logarithms with assumptions:

Logarithm of a product:

Change of base:

Expand assuming real variables x and y:

Applications  (2)

Find the real exponent of a nonzero number:

Evaluate the transform at a point:

Plot the spectrum:

Plot both the spectrum and the plot phase using color:

Plot the spectrum in the complex plane using ParametricPlot3D:

Properties & Relations  (2)

Simplify the logarithm with assumptions:

Solve logarithmic equations:

Wolfram Research (2008), Log10, Wolfram Language function, https://reference.wolfram.com/language/ref/Log10.html.


Wolfram Research (2008), Log10, Wolfram Language function, https://reference.wolfram.com/language/ref/Log10.html.


Wolfram Language. 2008. "Log10." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Log10.html.


Wolfram Language. (2008). Log10. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Log10.html


@misc{reference.wolfram_2024_log10, author="Wolfram Research", title="{Log10}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Log10.html}", note=[Accessed: 13-July-2024 ]}


@online{reference.wolfram_2024_log10, organization={Wolfram Research}, title={Log10}, year={2008}, url={https://reference.wolfram.com/language/ref/Log10.html}, note=[Accessed: 13-July-2024 ]}