Logarithms
In mathematics, a logarithm is the inverse operation of exponentiation.
Just as subtraction is the inverse of addition, and division is the inverse of multiplication, a logarithm "undoes" an exponent.
If: b^x = y
Then: logb y = x
Where:
b is the base
x is the exponent
y is the result
logb (y) means: “What power should I raise b to in order to get y?”
: Since (2^3 = 8), then (log2 8 = 3).
Laws of Logarithms
Product Rule: logb (MN) = logb M + logb N
Example: (log (100)(1000) = log (100) + log (1000) = 2 + 3 = 5).
Quotient Rule: logb M/N = logb M - logb N)
Example: (log (1000/100) = log (1000) - log (100) = 3 - 2 = 1).
Power Rule: (logb (M^n) = n logb M)
Example: (log2 (8^2) = 2 log2(8) = 2 • 3 = 6).