ln - Maple Help

ln

The Natural Logarithm

log

The General Logarithm

log10

The Common Logarithm

log2

The Binary Logarithm

Calling Sequence

 ln(x) log(x) log10(x) log2(x) log[b](x) ${\mathrm{log}}_{b}\left(x\right)$ log(x, b)

Parameters

 x - expression b - base

Description

 • The natural logarithm, ln, is the logarithm with base $ⅇ=2.71828$...  For $0 we have $\mathrm{ln}\left(x\right)=y$ <==> $x={ⅇ}^{y}$.
 • For complex-valued expressions x, $\mathrm{ln}\left(x\right)=\mathrm{ln}\left(\left|x\right|\right)+I\mathrm{arg}\left(x\right)$, where $-\mathrm{\pi }$
 • The log function is the general logarithm.  For $0 and $0 we have ${\mathrm{log}}_{b}\left(x\right)=y$<==>$x={b}^{y}$.  log is extended to general complex b and x by ${\mathrm{log}}_{b}\left(x\right)=\frac{\mathrm{ln}\left(x\right)}{\mathrm{ln}\left(b\right)}$.
 • The default value of the base b is $ⅇ$.
 • You can enter the function log with base b using either the 1-D or 2-D calling sequence.  The base can be entered as an index or as the second argument.  Similarly, $e$ can also be entered as exp(1) in 1-D.  See exp for more about the exponential function.
 • $\mathrm{log10}\left(x\right)={\mathrm{log}}_{10}\left(x\right)$.
 • $\mathrm{log2}\left(x\right)={\mathrm{log}}_{2}\left(x\right)$.
 • $\mathrm{ln}\left(x\right)={\mathrm{log}}_{ⅇ}\left(x\right)$.

Examples

 > $\mathrm{ln}\left(1\right)$
 ${0}$ (1)
 > $\mathrm{diff}\left(\mathrm{ln}\left(x\right),x\right)$
 $\frac{{1}}{{x}}$ (2)
 > $\mathrm{ln}\left(3.14+2.71I\right)$
 ${1.422562238}{+}{0.7120258406}{}{I}$ (3)
 > $\mathrm{ln}\left(3+4I\right)$
 ${\mathrm{ln}}{}\left({3}{+}{4}{}{I}\right)$ (4)
 > $\mathrm{evalc}\left(\right)$
 ${\mathrm{ln}}{}\left({5}\right){+}{I}{}{\mathrm{arctan}}{}\left(\frac{{4}}{{3}}\right)$ (5)
 > $\mathrm{ln}\left(10000\right)$
 ${4}{}{\mathrm{ln}}{}\left({10}\right)$ (6)

The default value of the base b is $ⅇ$.

 > $\mathrm{log}\left(10000\right)$
 ${4}{}{\mathrm{ln}}{}\left({10}\right)$ (7)
 > $\mathrm{log}\left(\mathrm{exp}\left(3\right)\right)$
 ${3}$ (8)
 > $\mathrm{log10}\left(10000\right)$
 ${4}$ (9)
 > $\mathrm{log}\left[10\right]\left(100\right)$
 ${2}$ (10)
 > $\mathrm{log}\left(16,8\right)$
 $\frac{{4}}{{3}}$ (11)
 > $\mathrm{log}\left[\mathrm{exp}\left(1\right)\right]\left(x\right)$
 ${\mathrm{ln}}{}\left({x}\right)$ (12)
 > $\mathrm{log}\left[b\right]\left(x\right)$
 $\frac{{\mathrm{ln}}{}\left({x}\right)}{{\mathrm{ln}}{}\left({b}\right)}$ (13)
 > $\mathrm{log10}\left(65\right)$
 $\frac{{\mathrm{ln}}{}\left({65}\right)}{{\mathrm{ln}}{}\left({10}\right)}$ (14)
 > $\mathrm{log2}\left(\mathrm{exp}\left(1\right)\right)$
 $\frac{{1}}{{\mathrm{ln}}{}\left({2}\right)}$ (15)
 > $\mathrm{evalf}\left(\right)$
 ${1.442695041}$ (16)
 > $\mathrm{log}\left[5\right]\left(5x\right)-\mathrm{log}\left[5\right]\left(x\right)$
 $\frac{{\mathrm{ln}}{}\left({5}{}{x}\right)}{{\mathrm{ln}}{}\left({5}\right)}{-}\frac{{\mathrm{ln}}{}\left({x}\right)}{{\mathrm{ln}}{}\left({5}\right)}$ (17)
 > $\mathrm{simplify}\left(\right)$
 ${1}$ (18)
 > $\mathrm{solve}\left(\mathrm{log}\left[6\right]\left(2y\right)=2,y\right)$
 ${18}$ (19)
 > $\mathrm{convert}\left(\mathrm{arcsin}\left(x\right),\mathrm{ln}\right)$
 ${-I}{}{\mathrm{ln}}{}\left({I}{}{x}{+}\sqrt{{-}{{x}}^{{2}}{+}{1}}\right)$ (20)

Compatibility

 • The log2 command was introduced in Maple 2021.