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Log Function

System.Math

## Syntax

`Math.Log(`d`)`

or:

`Math.Log(`a`, `newbase`)`
`d` or `a `(required; Double)

A numeric expression greater than zero

`newbase `(required; Double)

The base of the logarithm

Double

## Description

Returns the natural (base e) logarithm of a given number (the first syntax) or the logarithm of a given number in a specified base (the second syntax)

## Rules at a Glance

• The natural logarithm is the logarithm base e, a constant whose value is approximately 2.718282. The natural logarithm satisfies the equation:

`e^Log(x) = x`

In other words, the natural logarithm function is the inverse function of the exponential function.

• `d` or `a`, 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.”

• This is a Shared member, so it can be used without creating any objects.

## 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:

```Static Function Log10(X)
Log10 = Log(X) / Log(10#)
End Function```
• The inverse trigonometric functions, which are not intrinsic to VB, can be computed using the value returned by the Log function. The functions and their formulas are:

Inverse hyperbolic ...

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