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. For example, if b^y = x, then log_b(x) = y.

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CCSS.HSF.BF.B.5

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. Common bases include 10 (common logarithm) and e (natural logarithm).

Front

What is the product property of logarithms?

Back

The product property states that log_b(MN) = log_b(M) + log_b(N), meaning the logarithm of a product is the sum of the logarithms.

Front

What is the quotient property of logarithms?

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The quotient property states that log_b(M/N) = log_b(M) - log_b(N), meaning the logarithm of a quotient is the difference of the logarithms.

Front

What is the power property of logarithms?

Back

The power property states that log_b(M^p) = p * log_b(M), meaning the logarithm of a number raised to a power is the power times the logarithm of the number.

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What is the change of base formula?

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

What is the definition of a common logarithm?

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A common logarithm is a logarithm with base 10, denoted as log(x) or log_10(x).

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What is the definition of a natural logarithm?

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A natural logarithm is a logarithm with base e (approximately 2.718), denoted as ln(x).

Front

How do you solve log equations?

Back

To solve log equations, you can rewrite the logarithmic equation in exponential form and then solve for the variable.

Front

What is the logarithm of 1?

Back

The logarithm of 1 in any base is always 0, because any number raised to the power of 0 equals 1.