Solving Exponentials Using Logarithms

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What is an exponent?

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An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

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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 produce a given number. For example, log_b(a) = c means b^c = a.

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What is the relationship between exponents and logarithms?

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Logarithms and exponents are inverse operations. If b^x = y, then log_b(y) = x.

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What is the change of base formula for logarithms?

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The change of base formula allows you to convert a logarithm to a different base: log_b(a) = log_k(a) / log_k(b), where k is any positive number.

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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, isolate the variable, and then solve for it.

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What is the natural logarithm?

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The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828.

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What is the common logarithm?

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The common logarithm is the logarithm to the base 10, denoted as log(x). It is often used in scientific calculations.

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How do you express an exponential function in logarithmic form?

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To express an exponential function in logarithmic form, rewrite b^x = y as log_b(y) = x.

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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). 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(m / n) = log_b(m) - log_b(n). This means the logarithm of a quotient is the difference of the logarithms.