Expanding and Condensing Logarithms

Front

What is the product rule for logarithms?

Back

log_b(mn) = log_b(m) + log_b(n)

Front

What is the quotient rule for logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n)

Front

What is the power rule for logarithms?

Back

log_b(m^k) = k * log_b(m)

Front

How do you expand the logarithm of a product?

Back

Use the product rule: log_b(mn) = log_b(m) + log_b(n)

Front

How do you expand the logarithm of a quotient?

Back

Use the quotient rule: log_b(m/n) = log_b(m) - log_b(n)

Front

How do you expand the logarithm of a power?

Back

Use the power rule: log_b(m^k) = k * log_b(m)

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.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

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

Back

Use the product rule: log_b(m) + log_b(n) = log_b(mn)

Front

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

Back

Use the quotient rule: log_b(m) - log_b(n) = log_b(m/n)