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#### Search: #### Log

Function: log (<x>) Represents the natural (base e) logarithm of <x>. Maxima does not have a built-in function for the base 10 logarithm or other bases. `log10(x) := log(x) / log(10)` is a useful definition.

Simplification and evaluation of logarithms is governed by several global flags:

`logexpand` - causes `log(a^b)` to become `b*log(a)`. If it is set to `all`, `log(a*b)` will also simplify to `log(a)+log(b)`. If it is set to `super`, then `log(a/b)` will also simplify to `log(a)-log(b)` for rational numbers `a/b`, `a#1`. (`log(1/b)`, for `b` integer, always simplifies.) If it is set to `false`, all of these simplifications will be turned off.

`logsimp` - if `false` then no simplification of `%e` to a power containing `log`s is done.

`lognumer` - if `true` then negative floating point arguments to `log` will always be converted to their absolute value before the `log` is taken. If `numer` is also `true`, then negative integer arguments to `log` will also be converted to their absolute value.

`lognegint` - if `true` implements the rule `log(-n)` -> `log(n)+%i*%pi` for `n` a positive integer.

`%e_to_numlog` - when `true`, `r` some rational number, and `x` some expression, `%e^(r*log(x))` will be simplified into `x^r` . It should be noted that the `radcan` command also does this transformation, and more complicated transformations of this ilk as well. The `logcontract` command "contracts" expressions containing `log`.

There are also some inexact matches for `log`. Try `?? log` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

##### log

f(x):= (11*x^3+60*x^2...

f(9.0);

log(10);

Calculate

##### log

3 * log(2/1.2)/log(14...

Calculate

##### log-plot2d f:log(x-1);

plot2d(f,[x,-2,2],[y,...

Calculate

##### log-sum

s(n,k) := sum(n!/(kk!...

log(1.0 * (s(288, 128...

2.0^288/s(288, 128);

Calculate

Calculate

##### log-plot2d plot2d ((log(x)-1/(x*...

Calculate

##### log-rat-ratsimpexpons-subst-true

a:(x^k-1)/(2^k-1);

b:(x^k-x-1)/(2^k-2);

c: rat(b-a);

Calculate

##### log-plot3d plot3d(log(x^2*y^2),[...

Calculate

log(7);

Calculate

##### log-plot2d-taylor-tex f(x):=(log(x))/(log(1...

T1(x):=taylor(f(x), x...

T2(x):=taylor(f(x), x...

Calculate 