Expanding and Condensing Logs Practice

Front

What is the product rule for logarithms?

Back

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

Front

What is the quotient rule for 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 for logarithms?

Back

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

Condense the expression: log_5(3) + log_5(6) + log_5(9).

Back

log_5(162) using the product rule.

Front

Expand the expression: log_5(30).

Back

log_5(30) = log_5(3) + log_5(10) using the product rule.

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.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

What is the value of log_10(100)?

Back

2, because 10^2 = 100.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.