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(mn) = log_b(m) + log_b(n).

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What is the quotient property of logarithms?

Back

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?

Back

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

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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 (x > 0).

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How do you solve log_b(x) + log_b(y) = c?

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Use the product property: log_b(xy) = c, then rewrite in exponential form: xy = b^c.

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What is the significance of the base in logarithms?

Back

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

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How do you solve log_b(x) = log_b(y)?

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If log_b(x) = log_b(y), then x = y.