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# Logarithmic Functions

Use the following functions for performing various logarithmic calculations.

## log

Returns the natural logarithm of a given number. The log function is the inverse of the exp function.

Syntax: | log(Number)
Arguments: | Number is the positive number of which you want the natural logarithm.
Examples: | log(1) returns 0. log(2) returns 0.6931. log(exp(5)) returns 5. log(256) / log(2) returns 8. log(frame / 20) * 50 yields the following curve:

## log10

Returns the base-10 logarithm of a given number.

Syntax: | log10(Number)
Arguments: | Number is the positive number of which you want the base-10logarithm.
Examples: | log10(1) returns 0. log10(10) returns 1. log10(100) returns 2.

## log1p

Returns the natural logarithm of 1 plus a given number. The log1p function is the inverse of the expm1 function.

Syntax: | log1p(Number)
Arguments: | Number is the positive number less 1 of which you want the natural logarithm.
Examples: | log(0) returns 0. log(1) returns 0.6931. log1p(expm1(5)) returns 5. log1p(frame) returns the equivalent of log(1+frame). log1p(frame / 20) * 50 yields the following curve:

## exp

Returns the constant e (the base of the natural logarithm) raised to the power of a given number. The exp function is the inverse of the log function.

Syntax: | exp(Number)
Arguments: | Number is the exponent applied to the base e.
Examples: | exp(0) returns 1. exp(1) returns 2.7182. exp(2) returns 7.3890. exp(log(5)) returns 5. exp(frame / 20) * 5 yields the following curve:

## expm1

Returns the constant e (the base of the natural logarithm) raised to the power of a given number, minus 1. The expm1 function is the inverse of the log1p function.

Syntax: | expm1(Number)
Arguments: | Number is the exponent applied to the base e.
Examples: | expm1(0) returns 0. expm1(1) returns 1.7182. expm1(2) returns 6.3890. expm1(log1p(5)) returns 5. expm1(frame) returns the equivalent of exp(frame) - 1.