Properties of Logs

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What is the definition of a logarithm?

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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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What is the base of a logarithm?

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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?

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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.

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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.

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What is the power property of logarithms?

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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?

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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.

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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).

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How do you solve log equations?

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

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What is the logarithm of 1?

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