6.4 Properties of Logs

Front

What is the product rule of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) for any positive numbers M and N.

Front

What is the quotient rule of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) for any positive numbers M and N.

Front

What is the power rule of logarithms?

Back

log_b(M^p) = p * log_b(M) for any positive number M and real number p.

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the value of log_b(b)?

Back

log_b(b) = 1, because b raised to the power of 1 equals b.

Front

What is the value of log_b(1)?

Back

log_b(1) = 0, because b raised to the power of 0 equals 1.

Front

What does it mean if log_b(a) is negative?

Back

It means that a is between 0 and 1, since b raised to a negative exponent results in a fraction.

Front

Expand the logarithm: log(4x)

Back

log(4) + log(x) using the product rule.

Front

Condense the expression: log(4) + log(x)

Back

log(4x) using the product rule.

Front

What is the value of log_9(1/30)?

Back

Negative, because 1/30 is less than 1.