Properties of Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

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

Front

What is the product property of logarithms?

Back

The product property states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power property of logarithms?

Back

The power property states that log_b(m^p) = p * log_b(m).

Front

How do you expand log_b(m * n)?

Back

Using the product property: log_b(m * n) = log_b(m) + log_b(n).

Front

How do you condense log_b(m) + log_b(n)?

Back

Using the product property: log_b(m) + log_b(n) = log_b(m * n).

Front

How do you condense log_b(m) - log_b(n)?

Back

Using the quotient property: log_b(m) - log_b(n) = log_b(m / n).

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4.

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.