log()

log(x, base = exp(1))

The log() function computes the natural logarithm (base e) of a number. The natural logarithm uses Euler’s number e as its base.

Syntax

log(x, base = exp(1))

Parameters

Parameter	Type	Default	Description
x	numeric	—	A numeric vector or scalar
base	numeric	exp(1)	The base for the logarithm

Examples

Basic usage

# Natural log of e is 1
log(exp(1))
# [1] 1

# Natural log of 1 is 0
log(1)
# [1] 0

# Natural log of values > 1
log(1:5)
# [1] 0.000000 0.693147 1.098612 1.386294 1.609438

# Natural log of values < 1 (negative result)
log(0.5)
# [1] -0.6931472

Using different bases

# Log base 2
log(8, base = 2)
# [1] 3

# Log base 10
log(100, base = 10)
# [1] 2

Common bases shortcuts

# log10() is log(x, base = 10)
log10(100)
# [1] 2

# log2() is log(x, base = 2)
log2(8)
# [1] 3

Common Patterns

Log-transforming skewed data

# Log-transform skewed distribution
x <- c(1, 10, 100, 1000, 10000)
log(x)
# [1] 0.000000 2.302585 4.605170 6.907755 9.210340

Geometric mean

# Geometric mean using exp(mean(log(x)))
x <- c(2, 4, 8)
exp(mean(log(x)))
# [1] 4

Log-odds to probability

# Convert log-odds to probability
log_odds <- 0.5
exp(log_odds) / (1 + exp(log_odds))
# [1] 0.6224593

See Also

• base::exp
• base::log10
• base::log2
• base::log1p