Log Calculator (Logarithm)

What is Log?

The logarithm, or log, is the inverse of exponentiation. It is the number that a fixed base must be raised to to yield the number. Conventionally, log implies base 10, but "e" (ln) or base 2 are also used. If x = b^y, then y = log_b x.

• Base 10: Common in science and engineering.
• Base e (ln): Used in math and physics.
• Base 2: Used in computer science.

Basic Log Rules

log_b(x × y) = log_b x + log_b y
EX: log(1 × 10) = log(1) + log(10) = 0 + 1 = 1

log_b(x / y) = log_b x - log_b y
EX: log(10 / 2) = log(10) - log(2) = 1 - 0.301 = 0.699

log_b(x^y) = y × log_b x
EX: log(2^6) = 6 × log(2) = 1.806

log_b x = log_k x / log_k b
EX: log_10 x = log_2 x / log_2 10

log_b c = 1 / log_c b
EX: log_5 2 = 1 / log_2 5

Other notes: log_b 1 = 0, log_b b = 1, log_b 0 = undefined, lim x→0 log_b x = -∞, ln(e^x) = x