Product and Quotient Rule of Logarithms

Front

What is the Product Rule of Logarithms?

Back

The Product Rule states that the logarithm of a product is equal to the sum of the logarithms of the factors. Mathematically, log_b(MN) = log_b(M) + log_b(N).

Front

What is the Quotient Rule of Logarithms?

Back

The Quotient Rule states that the logarithm of a quotient is equal to the difference of the logarithms. Mathematically, log_b(M/N) = log_b(M) - log_b(N).

Front

If log_2(8) = x, what is the value of x?

Back

x = 3, because 2^3 = 8.

Front

Using the Product Rule, simplify log_3(9) + log_3(4).

Back

log_3(9 * 4) = log_3(36).

Front

Using the Quotient Rule, simplify log_5(25) - log_5(5).

Back

log_5(25/5) = log_5(5) = 1.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. In log_b(a), b is the base.

Front

How do you express log_b(M^n) using logarithmic properties?

Back

log_b(M^n) = n * log_b(M) (Power Rule).

Front

If log_10(1000) = x, what is the value of x?

Back

x = 3, because 10^3 = 1000.

Front

What is the relationship between exponential and logarithmic functions?

Back

Logarithmic functions are the inverses of exponential functions. If y = b^x, then x = log_b(y).

Front

Using the Product Rule, what is log_2(16) + log_2(4)?

Back

log_2(16 * 4) = log_2(64) = 6.