Expanding and Condensing Logs

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. It is the inverse operation of exponentiation.

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(MN) = log_b(M) + log_b(N), where b is the base.

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(M/N) = log_b(M) - log_b(N), where b is the base.

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M), where b is the base.

Front

How do you condense the expression log_b(M) + log_b(N)?

Back

You can condense it to log_b(MN) using the product rule.

Front

How do you condense the expression log_b(M) - log_b(N)?

Back

You can condense it to log_b(M/N) using the quotient rule.

Front

How do you expand the expression log_b(M^p)?

Back

You can expand it to p * log_b(M) using the power rule.

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

What is the value of log_b(b)?

Back

The value of log_b(b) is 1, since b raised to the power of 1 equals b.

Front

What is the value of log_b(1)?

Back

The value of log_b(1) is 0, since b raised to the power of 0 equals 1.