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.

Tags

CCSS.HSF.BF.B.5

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.