Properties of Logarithms

Front

What is the Product Property of Logarithms?

Back

The Product Property states that log_b(mn) = log_b(m) + log_b(n), meaning the logarithm of a product is the sum of the logarithms.

Front

What is the Quotient Property of Logarithms?

Back

The Quotient Property states that log_b(m/n) = log_b(m) - log_b(n), meaning the logarithm of a quotient is the difference of the logarithms.

Front

What is the Power Property of Logarithms?

Back

The Power Property states that log_b(m^p) = p * log_b(m), meaning the logarithm of a number raised to a power is the power times the logarithm of the number.

Front

Condense: log_a(x) + log_a(y)

Back

log_a(xy) using the Product Property.

Front

Condense: log_b(x) - log_b(y)

Back

log_b(x/y) using the Quotient Property.

Front

Condense: 3 * log_c(x)

Back

log_c(x^3) using the Power Property.

Front

Write log_b(1) in terms of logarithms.

Back

log_b(1) = 0, because any number raised to the power of 0 equals 1.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

Condense: log_5(3) + log_5(6) + log_5(9)

Back

log_5(162) using the Product Property.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number, expressed as log_b(a) = c if b^c = a.