Properties of Logs

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. It is expressed as log_b(a) = c, meaning b^c = a.

Front

What are the properties of logarithms?

Back

The main properties of logarithms include: 1) Product Property: log_b(xy) = log_b(x) + log_b(y); 2) Quotient Property: log_b(x/y) = log_b(x) - log_b(y); 3) Power Property: log_b(x^n) = n * log_b(x).

Front

What is the Product Property of logarithms?

Back

The Product Property states that the logarithm of a product is equal to the sum of the logarithms of the factors: log_b(xy) = log_b(x) + log_b(y).

Front

What is the Quotient Property of logarithms?

Back

The Quotient Property states that the logarithm of a quotient is equal to the difference of the logarithms: log_b(x/y) = log_b(x) - log_b(y).

Front

What is the Power Property of logarithms?

Back

The Power Property states that the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the base: log_b(x^n) = n * log_b(x).

Front

What is the change of base formula for logarithms?

Back

The change of base formula allows you to convert logarithms from one base to another: log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

How do you evaluate log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

What is the logarithm of 1 in any base?

Back

The logarithm of 1 in any base is always 0: log_b(1) = 0, because b^0 = 1.