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Evaluate ln(x)
Evaluate log2x
Evaluate lognx
Evaluate n-th power
Evaluate n-th root
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Decimal logarithm calculator

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

This tool evaluates the decimal logarithm of a number: \(\log_{10}{x}\). Enter the argument x below.

x =
Result:
\(\log_{10}{x}\) =
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Definitions

General

The decimal (also called decadic) logarithm of a number x, is a power p so that 10p = x. In modern notation decimal logarithm is written as \(\log_{10}{x}\) or lg(x). Any positive real number has a decimal logarithm. The decimal logarithm of 1 is 0, while the decimal logarithm of 0 approaches negative infinity.

The graph of the decimal logarithm function is shown in the figure below. It is a monotonic function.

log10-graph

Properties

The derivative of the decimal logarithm function is:

\[ \left(\log_{10} x\right)' = \frac{1}{x}\frac{1}{\ln{10}} \approx \frac{0.4342945}{x} \]

The integral of the decimal logarithm function is given by:

\[ \int \log_{10} x\, \mathrm{d}x = \frac{x\ln{x}-x}{\ln{10}} +C \]

See also
Evaluate ln(x)
Evaluate log2x
Evaluate lognx
Evaluate n-th power
Evaluate n-th root
All evaluation tools