Log Function

Log Function

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Class

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

Return Value

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 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) = Log((Sgn(X) * Sqr(X * X + 1) +1) / X)

  Inverse hyperbolic cotangent

  HArccotan(X) = Log((X + 1) / (X - 1)) / 2

See Also

Exp Function, Log10 Function