Expanding and Condensing Logs

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

Condense: log_4(16) + log_4(4)

Back

log_4(64) because 16 * 4 = 64.

Front

Expand: log_5(25x)

Back

2 + log_5(x) because log_5(25) = 2.

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: 3log_2(8) - log_2(4)

Back

log_2(32) because 3log_2(8) = log_2(512) and log_2(512) - log_2(4) = log_2(512/4) = log_2(128).

Front

Expand: log_3(9x^2)

Back

2 + log_3(x^2) = 2 + 2log_3(x).

Front

What does it mean to condense logarithmic expressions?

Back

To combine multiple logarithmic terms into a single logarithm using logarithmic properties.

Front

What does it mean to expand logarithmic expressions?

Back

To break down a single logarithmic term into multiple terms using logarithmic properties.