Properties of Logarithms

Front

What is the product property of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y) - This property states that the logarithm of a product is the sum of the logarithms of the factors.

Front

What is the quotient property of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y) - This property states that the logarithm of a quotient is the difference of the logarithms.

Front

What is the power property of logarithms?

Back

log_b(x^k) = k * log_b(x) - This property states that the logarithm of a number raised to a power is the power times the logarithm of the number.

Front

How do you condense the expression log_a(x) + log_a(y)?

Back

log_a(xy) - This uses the product property of logarithms.

Front

How do you condense the expression log_a(x) - log_a(y)?

Back

log_a(x/y) - This uses the quotient property of logarithms.

Front

How do you express log_b(x^3) using the power property?

Back

3 * log_b(x) - This uses the power property of logarithms.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive k - This allows you to change the base of a logarithm.

Front

If log_b(2) = p and log_b(3) = q, how can you express log_b(6)?

Back

log_b(6) = log_b(2*3) = log_b(2) + log_b(3) = p + q - This uses the product property.

Front

What is the value of log_10(1000)?

Back

3 - Because 10^3 = 1000.

Front

What is the value of log_2(8)?

Back

3 - Because 2^3 = 8.