Solving Logarithmic Equations

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What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

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What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

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What is the product property of logarithms?

Back

The product property states that log_b(m * n) = log_b(m) + log_b(n).

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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).

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What is the power property of logarithms?

Back

The power property states that log_b(m^p) = p * log_b(m).

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How do you solve the equation log_b(x) = c?

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To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

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What is the definition of a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable or expression.

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How do you combine logarithmic expressions?

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Use the product, quotient, and power properties to combine logarithmic expressions into a single logarithm.

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What is the domain of a logarithmic function?

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The domain of a logarithmic function is the set of positive real numbers, as logarithms are undefined for zero and negative numbers.

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What is the significance of the base in logarithms?

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The base of a logarithm determines the rate of growth of the logarithmic function; common bases are 10 (common logarithm) and e (natural logarithm).