Logarithms

If a^b = c (where

If a^b = c (where a ≠ 1), then b is called the logarithm of c at base a, written as log_a c = b. This means logarithm answers the question: 'To what p

Any exponential equation a^b = c

Any exponential equation a^b = c can be written as log_a c = b (logarithmic form) and vice versa. For example: 2^3 = 8 ⟺ log_2 8 = 3

log_a(m × n) = log_a m

log_a(m × n) = log_a m + log_a n. The logarithm of a product equals the sum of logarithms of individual factors

log_a(m/n) = log_a m

log_a(m/n) = log_a m - log_a n. The logarithm of a quotient equals the difference of logarithms

log_a(m^n) = n × log_a m

log_a(m^n) = n × log_a m. The logarithm of a power equals the exponent multiplied by the logarithm of the base number