Properties of Logarithms

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. For example, log_b(a) = c means b^c = a.

Front

State the Product Property of Logarithms.

Back

The Product Property states that log_b(xy) = log_b(x) + log_b(y).

Front

State the Quotient Property of Logarithms.

Back

The Quotient Property states that log_b(x/y) = log_b(x) - log_b(y).

Front

State the Power Property of Logarithms.

Back

The Power Property states that log_b(x^n) = n * log_b(x).

Front

Expand log_6(5x^3/y).

Back

log_6(5) + 3*log_6(x) - log_6(y).

Front

Rewrite log_b(xy) as two logs.

Back

log_b(x) + log_b(y).

Front

Rewrite log_b(x/y) as two logs.

Back

log_b(x) - log_b(y).

Front

Rewrite log_b(x^n).

Back

n * log_b(x).

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.

Front

What is the change of base formula?

Back

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