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Log Function

Syntax

`Log(`number`)`
`number`

Use: Required

Data Type: Double

A numeric expression greater than zero.

A Double.

Description

Returns the natural logarithm of a given number.

Rules at a Glance

• The natural logarithm is based on `e`, a constant whose value is approximately 2.718282. The natural logarithm is expressed by the equation:

`ez = x`

where `z` `=` `Log(x)`. In other words, the natural logarithm is the inverse of the exponential function.

• `number`, the value whose natural logarithm the function is to return, must be a positive real number. If number is negative or zero, the function generates runtime error 5, “Invalid procedure call or argument.”

Programming Tips and Gotchas

• You can calculate base-`n` logarithms for any number `x`, by dividing the natural logarithm of `x` by the natural logarithm of `n`, as the following expression illustrates:

`Log`n`(`x`) = Log(`x`) / Log(`n`)`

For example, the Log10 function shows the source code for a custom function that calculates base-10 logarithms:

```Function Log10(X)
Log10 = Log(X) / Log(10)
End Function```
• A number of other mathematical functions that aren’t intrinsic to VBScript can be computed using the value returned by the Log function. The functions and their formulas are:

Inverse Hyperbolic Sine

`HArcsin(X)` `=` `Log(X` `+` `Sqr(X` `*` `X` `+` `1))`

Inverse Hyperbolic Cosine

`HArccos(X)` `=` `Log(X` `+` `Sqr(X` `*` `X` `-` `1))`

Inverse Hyperbolic Tangent

`HArctan(X)` `=` `Log((1` `+` `X)` `/` `(1` `-` `X))` `/` `2`

Inverse Hyperbolic Secant

`HArcsec(X)` `=` `Log((Sqr(-X` `*` `X` `+` `1)` `+` `1)` `/` `X)`

Inverse Hyperbolic Cosecant

`HArccosec(X) ...`

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