math.log

local result = math.log(
    value,
    base = math.exp(1)
)

Type	Name	Description
`number`	value	Positive number to compute the logarithm of
`number`	base	Logarithm base - defaults to e (natural log)

Type	Name	Description
`number`	result	Logarithm of value in the given base

Natural log of e

local result = math.log(math.exp(1))

engine.print("info", result) -- 1.0

Natural log of 1 is always 0

local result = math.log(1)

engine.print("info", result) -- 0.0

Log base 10

local result = math.log(1000, 10)

engine.print("info", result) -- 3.0

Log base 2

local result = math.log(8, 2)

engine.print("info", result) -- 3.0

Compute number of digits in an integer

local n = 12345
local digits = math.floor(math.log(n, 10)) + 1

engine.print("info", digits) -- 5

Compute how many doublings to reach a target

local start = 1
local target = 1024
local doublings = math.ceil(math.log(target / start, 2))

engine.print("info", doublings) -- 10

Verify log and exp are inverses

local value = 5.0
local result = math.log(math.exp(value))

engine.print("info", result) -- 5.0