Log10

The base-10 (common) logarithm of z.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageLog10✓↗

Log10(z)the base-10 logarithm of z, $\log_{10}(z)$.

SageMathlog(z, 10)✓↗SymPylog(z, 10)↗mpmathlog10(z)Juliaenumeratio_ball(_log10, z)Rustlog10(z)

Typed signatures

Type	Package	Applies
(number) -> number	compute-engine	always

Domain: Elementary functions

Details

• Equivalent to Log(z, 10) and to compute-engine's default-base Log(z).
• Same exact-power-of-the-base fold in either direction as Log2.

Plot

Examples

Basic #

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In$\log_{10}(1\,000)$Out$3$

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In$\log_{10}(1)$Out$0$

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In$\log_{10}(100\,000)$Out$5$

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In$\log_{10}(1\,000\,000)$Out$6$

N(...) for a decimal value

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In$N(\log_{10}(2))$Out$0.301\,029\,995\,663\,981\,195\,214$

With one argument, log is base 10 and stays symbolic

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In$\log_{10}(2)$Out$\log_{10}(2)$

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In$\operatorname{Series}(\log_{10}(x+1), x, 0, 5)$Out$\frac{x}{\ln(10)}-\frac{x^2}{2\ln(10)}+\frac{x^3}{3\ln(10)}-\frac{x^4}{4\ln(10)}+\frac{x^5}{5\ln(10)}+O\left(x^6\right)$

Scope #

An exact negative power of 10 folds too: $\log_{10} \tfrac1{100} = -2$

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In$\log_{10}(\frac{1}{100})$Out$-2$

A symbolic argument becomes compute-engine's default-base Log

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In$\log_{10}(x)$Out$\log_{10}(x)$

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In$\log_{10}(5.5)$Out$0.740\,362\,689\,494\,243\,845\,536$

Threads element-wise over a list

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In$\log_{10}(\bigl\lbrack1, 10, 100, 1\,000\bigr\rbrack)$Out$\bigl\lbrack0, 1, 2, 3\bigr\rbrack$

Element-wise over a matrix, including the exact $\tfrac1{100}$ entry

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In$\log_{10}(\bigl\lbrack\bigl\lbrack1, 100\bigr\rbrack, \bigl\lbrack0, \frac{1}{100}\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, 2\bigr\rbrack, \bigl\lbrack-∞, -2\bigr\rbrack\bigr\rbrack$

As with Ln, the logarithm of complex infinity is $+\infty$

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In$\log_{10}(\tilde∞)$Out$∞$

Interval arithmetic: $\log_{10}[\tfrac13, 2] = [\log_{10} \tfrac13, \log_{10} 2]$

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In$\log_{10}(\mathrm{Interval}(\frac{1}{3}, 2))$Out$\mathrm{Interval}(\log_{10}(\frac{1}{3}), \log_{10}(2))$

Uncertainty propagation, to first order: $\log_{10}(\tfrac1{101} \pm 0.01) \approx -2.00 \pm 0.44$

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In$\log_{10}(\mathrm{Around}(\frac{1}{101}, 0.01))$Out$\mathrm{Around}(-2.004\,321\,373\,782\,642\,6, 0.438\,637\,426\,722\,284\,34)$

Derivative: $\frac{1}{x\ln 10}$

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In$\frac{\mathrm{d}\log_{10}(x)}{\mathrm{d}x}$Out$\frac{1}{x\ln(10)}$

To 30 significant digits, every one correctly rounded

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In$N(\log_{10}(7), 30)$Out$0.845\,098\,040\,014\,256\,830\,712\,216\,258\,593$

Another exact base-10 logarithm, unevaluated

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In$\log_{10}(5)$Out$\log_{10}(5)$

A 100-digit decimal logarithm

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In$N(\log_{10}(45), 100)$Out$1.653\,212\,513\,775\,343\,679\,376\,316\,911\,785\,737\,591\,632\,067\,846\,919\,283\,188\,349\,303\,819\,483\,350\,116\,292\,897\,736\,599\,009\,459\,177\,046\,431$

A complex argument gives a complex float

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In$N(\log_{10}(4+i))$Out$0.615\,224\,460\,689\,136\,9+0.106\,392\,881\,580\,032\,71i$

A matrix function with eigenvalues 1 and $\frac1{100}$ gives the exact integers 0 and $-2$

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In$\mathrm{FullSimplify}(\mathrm{MatrixFunction}(\mathrm{Log10}, \bigl\lbrack\bigl\lbrack1, 100\bigr\rbrack, \bigl\lbrack0, 1/100\bigr\rbrack\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack0, \frac{20\,000}{99}\bigr\rbrack, \bigl\lbrack0, -2\bigr\rbrack\bigr\rbrack$

$\log\infty=\infty$

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In$\log_{10}(∞)$Out$∞$

The log of 0 is $-\infty$

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In$\log_{10}(0)$Out$-∞$

Applications #

A float argument folds even for a fractional power of 10

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In$\log_{10}(0.001)$Out$-3.0$

Properties #

Same as compute-engine's default-base Log

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In$\log_{10}(1\,000)=\log_{10}(1\,000)$Out$\mathrm{True}$

About

Examples	25
Checked against	Wolfram Language 25 agreeSageMath 22 agreeSymPy 21 agree3 differmpmath 18 agreeJulia 15 agree3 errorRust 14 agree2 error
Crosswalk	Wolfram LanguageSageMathSymPympmathJuliaRust

Implementation

mappedsympypackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts

See also: Log, Log2, Lb