HW 3.4 Exponent & Log Equations

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What is the general form of an exponential equation?

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An exponential equation is generally in the form of y = a * b^(x), where a is a constant, b is the base (a positive real number), and x is the exponent.

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How do you solve an exponential equation of the form a * b^(x) = c?

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To solve an exponential equation of the form a * b^(x) = c, first isolate the exponential term (b^(x)), then take the logarithm of both sides and solve for x.

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What is the natural logarithm and how is it denoted?

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The natural logarithm is the logarithm to the base e, denoted as ln(x). It is the inverse function of the exponential function e^x.

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What is the relationship between logarithms and exponents?

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Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

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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 logarithmic equations?

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To solve logarithmic equations, you can exponentiate both sides to eliminate the logarithm, then solve the resulting equation.

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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. For example, in log_b(a), b is the base.

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What is the product rule for logarithms?

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The product rule states that log_b(xy) = log_b(x) + log_b(y). This means the logarithm of a product is the sum of the logarithms.

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What is the quotient rule for logarithms?

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The quotient rule states that log_b(x/y) = log_b(x) - log_b(y). This means the logarithm of a quotient is the difference of the logarithms.

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What is the power rule for logarithms?

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The power rule states that log_b(x^k) = k * log_b(x). This means the logarithm of a number raised to a power is the power times the logarithm of the number.