Expanding and Condensing Logarithms

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^k) = k * log_b(m) for any positive number m and any real number k.

Front

Expand: log_8(xy)

Back

log_8(x) + log_8(y) using the product rule.

Front

Expand: log_8(x^5)

Back

5 * log_8(x) using the power rule.

Front

Condense: log_8(x) + log_8(y)

Back

log_8(xy) using the product rule.

Front

Condense: 3 * log_8(x) - 2 * log_8(y)

Back

log_8(x^3/y^2) using the quotient and power rules.

Front

Expand: log_6(y) - log_6(2)

Back

log_6(y/2) using the quotient rule.

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

Expand: 6log_8(u) - 2log_8(v)

Back

log_8(u^6) - log_8(v^2) using the power rule.