Expanding and Condensing 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

What is the product rule of logarithms?

Back

The product rule states that log_b(MN) = log_b(M) + log_b(N).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(M/N) = log_b(M) - log_b(N).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(M^k) = k * log_b(M).

Front

Expand log_b(MN) using the product rule.

Back

log_b(MN) = log_b(M) + log_b(N).

Front

Expand log_b(M/N) using the quotient rule.

Back

log_b(M/N) = log_b(M) - log_b(N).

Front

Expand log_b(M^k) using the power rule.

Back

log_b(M^k) = k * log_b(M).

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_b(M) + log_b(N).

Back

log_b(M) + log_b(N) = log_b(MN) using the product rule.

Front

Condense log_b(M) - log_b(N).

Back

log_b(M) - log_b(N) = log_b(M/N) using the quotient rule.