Log Function

Returns a Double specifying the natural logarithm of a number.

Syntax

Log(number)

Parameters

number (Required): Double or any valid numeric expression greater than zero
Must be positive (> 0)
Cannot be zero or negative
Error 5 "Invalid procedure call or argument" if number <= 0

Return Value

Returns a Double: - Natural logarithm (base e) of the number - Also known as ln(x) in mathematics - Result can be positive, negative, or zero - Log(1) = 0 - Log(e) = 1 where e ≈ 2.71828182845905 - For values 0 < x < 1, result is negative - For values x > 1, result is positive

Remarks

The Log function returns the natural logarithm:

Natural logarithm uses base e (Euler's number)
e ≈ 2.71828182845905
Also written as ln(x) in mathematical notation
Inverse operation of Exp function
Log(Exp(x)) = x
Exp(Log(x)) = x (for x > 0)
To calculate logarithms with other bases, use change of base formula
Log base 10: Log(x) / Log(10)
Log base 2: Log(x) / Log(2)
Log base n: Log(x) / Log(n)
Error 5 if argument is zero or negative
Used in scientific and engineering calculations
Common in exponential growth/decay problems
Essential for statistical calculations
Used in information theory (entropy, information content)
Financial calculations (continuous compounding)
Physics (radioactive decay, sound levels)
Can be used to solve exponential equations
Part of VB6's math function library
Available in all VB versions

Typical Uses

Natural Logarithm

result = Log(10)

Base 10 Logarithm

log10 = Log(x) / Log(10)

Base 2 Logarithm

log2 = Log(x) / Log(2)

Exponential Decay

timeConstant = -1 / Log(decayRate)

Solve for Exponent

exponent = Log(result / initial) / Log(base)

Information Content

bits = -Log(probability) / Log(2)

pH Calculation

pH = -Log(hydrogenIonConcentration) / Log(10)

Continuous Compounding

rate = Log(finalValue / initialValue) / time

Basic Examples

Example 1: Natural Logarithm

Dim result As Double

result = Log(1)        ' Returns 0
result = Log(2.71828)  ' Returns ~1 (ln(e) = 1)
result = Log(10)       ' Returns ~2.302585
result = Log(100)      ' Returns ~4.605170

Example 2: Base 10 Logarithm

Function Log10(ByVal x As Double) As Double
Log10 = Log(x) / Log(10)
End Function

' Usage
Dim result As Double
result = Log10(100)    ' Returns 2
result = Log10(1000)   ' Returns 3
result = Log10(10)     ' Returns 1

Example 3: Exponential Growth

' Calculate doubling time
Function DoublingTime(ByVal growthRate As Double) As Double
' growthRate is the rate per time period (e.g., 0.05 = 5%)
DoublingTime = Log(2) / Log(1 + growthRate)
End Function

' Usage
Dim years As Double
years = DoublingTime(0.07)  ' 7% annual growth
MsgBox "Doubling time: " & Format(years, "0.0") & " years"

Example 4: Solve Exponential Equation

' Solve: base^exponent = result for exponent
Function SolveExponent(ByVal base As Double, _
ByVal result As Double) As Double
If base > 0 And base <> 1 And result > 0 Then
SolveExponent = Log(result) / Log(base)
Else
SolveExponent = 0
End If
End Function

' Usage: Solve 2^x = 32
Dim x As Double
x = SolveExponent(2, 32)  ' Returns 5
MsgBox "2^" & x & " = 32"

Common Patterns

Pattern 1: Log10 (Base 10 Logarithm)

Function Log10(ByVal x As Double) As Double
If x > 0 Then
Log10 = Log(x) / Log(10)
Else
Err.Raise 5, , "Invalid argument"
End If
End Function

Pattern 2: Log2 (Base 2 Logarithm)

Function Log2(ByVal x As Double) As Double
If x > 0 Then
Log2 = Log(x) / Log(2)
Else
Err.Raise 5, , "Invalid argument"
End If
End Function

Pattern 3: `LogN` (Logarithm with Any Base)

Function LogN(ByVal x As Double, ByVal base As Double) As Double
If x > 0 And base > 0 And base <> 1 Then
LogN = Log(x) / Log(base)
Else
Err.Raise 5, , "Invalid arguments"
End If
End Function

Pattern 4: `SafeLog`

Function SafeLog(ByVal x As Double, _
Optional ByVal defaultValue As Double = 0) As Double
On Error Resume Next
SafeLog = Log(x)
If Err.Number <> 0 Then
SafeLog = defaultValue
Err.Clear
End If
End Function

Pattern 5: `CalculateEntropy`

Function CalculateEntropy(probabilities() As Double) As Double
Dim i As Integer
Dim entropy As Double
Dim p As Double

entropy = 0
For i = LBound(probabilities) To UBound(probabilities)
p = probabilities(i)
If p > 0 Then
entropy = entropy - p * (Log(p) / Log(2))
End If
Next i

CalculateEntropy = entropy
End Function

Pattern 6: `CalculateHalfLife`

Function CalculateHalfLife(ByVal decayConstant As Double) As Double
If decayConstant > 0 Then
CalculateHalfLife = Log(2) / decayConstant
Else
CalculateHalfLife = 0
End If
End Function

Pattern 7: `CalculateDoublingTime`

Function CalculateDoublingTime(ByVal growthRate As Double) As Double
If growthRate > 0 Then
CalculateDoublingTime = Log(2) / Log(1 + growthRate)
Else
CalculateDoublingTime = 0
End If
End Function

Pattern 8: `SolveForTime` (Exponential Growth)

Function SolveForTime(ByVal initialValue As Double, _
ByVal finalValue As Double, _
ByVal rate As Double) As Double
If initialValue > 0 And finalValue > 0 And rate <> 0 Then
SolveForTime = Log(finalValue / initialValue) / rate
Else
SolveForTime = 0
End If
End Function

Pattern 9: `CalculateDecibels`

Function CalculateDecibels(ByVal power As Double, _
ByVal referencePower As Double) As Double
If power > 0 And referencePower > 0 Then
CalculateDecibels = 10 * (Log(power / referencePower) / Log(10))
Else
CalculateDecibels = 0
End If
End Function

Pattern 10: `CalculatePH`

Function CalculatePH(ByVal hydrogenIonConcentration As Double) As Double
If hydrogenIonConcentration > 0 Then
CalculatePH = -(Log(hydrogenIonConcentration) / Log(10))
Else
CalculatePH = 7  ' Neutral pH
End If
End Function

Advanced Examples

Example 1: Logarithm Calculator

' Module: LogarithmCalculator

Public Function NaturalLog(ByVal x As Double) As Double
If x <= 0 Then
Err.Raise 5, "LogarithmCalculator", _
"Argument must be positive"
End If
NaturalLog = Log(x)
End Function

Public Function Log10(ByVal x As Double) As Double
If x <= 0 Then
Err.Raise 5, "LogarithmCalculator", _
"Argument must be positive"
End If
Log10 = Log(x) / Log(10)
End Function

Public Function Log2(ByVal x As Double) As Double
If x <= 0 Then
Err.Raise 5, "LogarithmCalculator", _
"Argument must be positive"
End If
Log2 = Log(x) / Log(2)
End Function

Public Function LogBase(ByVal x As Double, _
ByVal base As Double) As Double
If x <= 0 Or base <= 0 Or base = 1 Then
Err.Raise 5, "LogarithmCalculator", _
"Invalid arguments"
End If
LogBase = Log(x) / Log(base)
End Function

Public Function Antilog(ByVal x As Double) As Double
' Returns e^x (inverse of Log)
Antilog = Exp(x)
End Function

Public Function Antilog10(ByVal x As Double) As Double
' Returns 10^x (inverse of Log10)
Antilog10 = 10 ^ x
End Function

Example 2: Exponential Growth Analyzer

' Class: GrowthAnalyzer
Private m_initialValue As Double
Private m_currentValue As Double
Private m_timeElapsed As Double

Public Sub Initialize(ByVal initialValue As Double)
m_initialValue = initialValue
m_currentValue = initialValue
m_timeElapsed = 0
End Sub

Public Property Let CurrentValue(ByVal value As Double)
m_currentValue = value
End Property

Public Property Let TimeElapsed(ByVal time As Double)
m_timeElapsed = time
End Property

Public Property Get GrowthRate() As Double
If m_timeElapsed > 0 And m_initialValue > 0 And m_currentValue > 0 Then
GrowthRate = Log(m_currentValue / m_initialValue) / m_timeElapsed
Else
GrowthRate = 0
End If
End Property

Public Property Get DoublingTime() As Double
Dim rate As Double
rate = GrowthRate

If rate > 0 Then
DoublingTime = Log(2) / rate
Else
DoublingTime = 0
End If
End Property

Public Function ProjectValue(ByVal futureTime As Double) As Double
Dim rate As Double
rate = GrowthRate

If rate <> 0 Then
ProjectValue = m_initialValue * Exp(rate * futureTime)
Else
ProjectValue = m_initialValue
End If
End Function

Public Function TimeToReach(ByVal targetValue As Double) As Double
Dim rate As Double
rate = GrowthRate

If rate > 0 And m_initialValue > 0 And targetValue > 0 Then
TimeToReach = Log(targetValue / m_initialValue) / rate
Else
TimeToReach = 0
End If
End Function

Example 3: Sound Level Calculator

' Module: SoundLevelCalculator
Private Const REFERENCE_PRESSURE As Double = 0.00002  ' 20 micropascals

Public Function CalculateDecibels(ByVal pressure As Double) As Double
If pressure > 0 Then
CalculateDecibels = 20 * (Log(pressure / REFERENCE_PRESSURE) / Log(10))
Else
CalculateDecibels = 0
End If
End Function

Public Function CombineSoundLevels(levels() As Double) As Double
Dim i As Integer
Dim sumPressures As Double
Dim pressure As Double

sumPressures = 0
For i = LBound(levels) To UBound(levels)
' Convert dB to pressure, sum, then convert back
pressure = REFERENCE_PRESSURE * Exp(levels(i) * Log(10) / 20)
sumPressures = sumPressures + pressure * pressure
Next i

If sumPressures > 0 Then
CombineSoundLevels = 10 * (Log(sumPressures) / Log(10)) + _
20 * (Log(REFERENCE_PRESSURE) / Log(10))
Else
CombineSoundLevels = 0
End If
End Function

Public Function CalculateDistance(ByVal soundLevelAtSource As Double, _
ByVal soundLevelAtDistance As Double, _
ByVal knownDistance As Double) As Double
Dim ratio As Double

' Sound decreases by 6 dB when distance doubles
ratio = (soundLevelAtSource - soundLevelAtDistance) / 6
CalculateDistance = knownDistance * (2 ^ ratio)
End Function

Example 4: Financial Calculator

' Module: FinancialCalculator

Public Function CalculateContinuousGrowthRate(ByVal initialValue As Double, _
ByVal finalValue As Double, _
ByVal years As Double) As Double
If initialValue > 0 And finalValue > 0 And years > 0 Then
CalculateContinuousGrowthRate = Log(finalValue / initialValue) / years
Else
CalculateContinuousGrowthRate = 0
End If
End Function

Public Function YearsToDouble(ByVal annualRate As Double) As Double
If annualRate > 0 Then
YearsToDouble = Log(2) / Log(1 + annualRate)
Else
YearsToDouble = 0
End If
End Function

Public Function EffectiveRate(ByVal nominalRate As Double, _
ByVal compoundingPeriods As Integer) As Double
If compoundingPeriods > 0 Then
EffectiveRate = Exp(compoundingPeriods * _
Log(1 + nominalRate / compoundingPeriods)) - 1
Else
EffectiveRate = 0
End If
End Function

Public Function CalculateAPY(ByVal principal As Double, _
ByVal finalAmount As Double, _
ByVal years As Double) As Double
If principal > 0 And finalAmount > 0 And years > 0 Then
CalculateAPY = Exp(Log(finalAmount / principal) / years) - 1
Else
CalculateAPY = 0
End If
End Function

Error Handling

' Error 5: Invalid procedure call or argument
On Error Resume Next
result = Log(0)
If Err.Number = 5 Then
MsgBox "Cannot take log of zero!"
End If

result = Log(-10)
If Err.Number = 5 Then
MsgBox "Cannot take log of negative number!"
End If

' Safe log function
Function SafeLog(ByVal x As Double) As Variant
On Error Resume Next
SafeLog = Log(x)
If Err.Number <> 0 Then
SafeLog = Null
Err.Clear
End If
End Function

Performance Considerations

Fast Operation: Log is a built-in processor instruction
Cache Constants: Store Log(10), Log(2) if used repeatedly
Avoid Division by Zero: Always validate arguments
Use Exp for Inverse: Exp(Log(x)) = x is optimized

Best Practices

Always validate that argument is positive
Use error handling for user input
Cache frequently used logarithms (Log(10), Log(2))
Document the base when using change of base formula
Use descriptive names for logarithm wrapper functions
Consider precision for very large or small numbers
Check for overflow in calculations
Use constants for common values (e, pi, etc.)
Validate results for domain-specific constraints
Comment formulas explaining mathematical relationships

Function	Purpose	Base	Domain
Log	Natural logarithm	e (2.718...)	x > 0
Exp	Exponential (e^x)	e	All reals
Log10	Common logarithm	10	x > 0
Log2	Binary logarithm	2	x > 0
^ (power)	Exponentiation	Variable	Depends

Common Logarithm Identities

' Log properties
Log(x * y) = Log(x) + Log(y)
Log(x / y) = Log(x) - Log(y)
Log(x ^ y) = y * Log(x)
Log(1) = 0
Log(e) = 1

' Change of base
Log_b(x) = Log(x) / Log(b)

' Inverse relationship
Exp(Log(x)) = x  (for x > 0)
Log(Exp(x)) = x

Platform Notes

Available in all VB6 versions
Part of VBA core library
Uses IEEE 754 double-precision floating point
Precision: approximately 15-16 significant digits
Range: 4.94065645841247E-324 to 1.79769313486232E+308
Behavior identical across Windows versions
CPU-level implementation (very fast)

Limitations

Positive Arguments Only: Cannot compute log of zero or negative numbers
Floating Point Precision: Subject to rounding errors
Very Small Numbers: May lose precision near zero
Very Large Numbers: May overflow in calculations
No Base Parameter: Must use change of base formula for other bases
Error for Invalid Input: Raises Error 5 instead of returning special value

Exp: Returns e raised to a power (inverse of Log)
Sqr: Returns square root
^: Exponentiation operator
Abs: Returns absolute value
Sgn: Returns sign of number