Log Function

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Named Arguments

No

Syntax

Log(number)

number

Use: Required

Data Type: Double

A numeric expression greater than zero.

Return Value

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:

  Logn(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

  
  

• A number of other mathematical functions that aren't intrinsic to VBA 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