Expand and Condense Logs Practice

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(MN) = log_b(M) + log_b(N), where M and N are positive numbers.

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(M/N) = log_b(M) - log_b(N), where M and N are positive numbers.

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

How do you expand the logarithm log_b(M^pN^q)?

Back

log_b(M^pN^q) = p * log_b(M) + q * log_b(N) using the power and product rules.

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.

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

What is the logarithmic form of an exponential equation?

Back

If b^y = x, then log_b(x) = y.