Exponential and Logarithmic Functions

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

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What is a logarithm?

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A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given 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. In log_b(x), b is the base.

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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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What is the product property of logarithms?

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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?

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

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How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in logarithmic form.

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What is continuous compounding?

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Continuous compounding refers to the process of earning interest on an investment continuously, calculated using the formula A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

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What is the range of an exponential function?

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The range of an exponential function f(x) = a * b^x (where a > 0) is (0, ∞) if b > 1, and (-∞, 0) if 0 < b < 1.