3.4 Solving Exponential and Logarithmic Equations

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What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.

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What is a logarithmic equation?

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A logarithmic equation is an equation that involves a logarithm of a variable. For example, log_b(x) = y means that b^y = x.

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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 to obtain a given number. In log_b(x), b is the base.

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What is the relationship between exponential and logarithmic functions?

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Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

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How do you solve the equation 3^x = 81?

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To solve 3^x = 81, rewrite 81 as 3^4. Therefore, x = 4.

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What is the change of base formula for logarithms?

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

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How do you solve log_2(x) = 5?

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To solve log_2(x) = 5, rewrite it in exponential form: x = 2^5, so x = 32.

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What is the product rule for 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 for 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 for logarithms?

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