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_7(xy)

Back

log_7(x) + log_7(y) (using the product rule).

Front

Expand: log_4(u/v)

Back

log_4(u) - log_4(v) (using the quotient rule).

Front

Expand: log_8(u^3)

Back

3 * log_8(u) (using the power 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: log_5(25)

Back

log_5(5^2) = 2 * log_5(5) = 2 (since log_5(5) = 1).

Front

Expand: log_2(8)

Back

log_2(2^3) = 3 * log_2(2) = 3 (since log_2(2) = 1).

Front

What is the definition of a logarithm?

Back

If b^y = x, then log_b(x) = y, where b > 0 and b ≠ 1.