Solve Log and Exponential Equations

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What is a logarithm?

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A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

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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. In log_b(a), b is the base.

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What is the product rule of logarithms?

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

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What is the quotient rule of logarithms?

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The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

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What is the power rule of logarithms?

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The power rule states that log_b(m^k) = k * log_b(m).

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How do you solve log equations?

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To solve log equations, you can use properties of logarithms to combine or separate logs, then convert to exponential form.

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What is an exponential equation?

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An exponential equation is an equation in which a variable appears in an exponent, such as a^x = b.

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How do you solve exponential equations?

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To solve exponential equations, you can take the logarithm of both sides or rewrite the equation in a form that allows for direct comparison.

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What is the change of base formula?

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The change of base formula allows you to compute logarithms with different bases: log_b(a) = log_k(a) / log_k(b) for any base k.

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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 log_b(x) is only defined for x > 0.