Exponential and Logarithm Laws

When multiplying exponential terms with the same base, add the exponents: a^(m+n)

When dividing exponential terms with the same base, subtract the exponents: a^(m-n)

When raising a power to another power, multiply the exponents: a^(mn)

The power of a product is the product of the powers: a^m * b^m

The power of a quotient is the quotient of the powers: a^m / b^m

Any non-zero number raised to the power of 0 is 1.

Relates fractional exponents to radicals

A negative exponent indicates the reciprocal of the base raised to the positive exponent

The logarithm of a product is the sum of the logarithms: log(a) + log(b)

The logarithm of a quotient is the difference of the logarithms: log(a) - log(b)

The logarithm of a number raised to a power is the product of the power and the logarithm of the number: n*log(b)

The logarithm of the base to itself is always 1.

The logarithm of 1 to any base is always 0.

Used to change the base of a logarithm to another base for simplification or calculation