PH: L3.4 Exponential and Logarithmic Equations

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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 the base (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.

Tags

CCSS.HSF.BF.B.5

Front

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 produce a given number. Common bases include 10 (common logarithm) and e (natural logarithm).

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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).

Tags

CCSS.HSF.BF.B.5

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k, allowing conversion between different logarithmic bases.

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What is the natural logarithm?

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The natural logarithm is the logarithm to the base e, denoted as ln(x). It is commonly used in calculus and mathematical analysis.

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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), allowing the simplification of the logarithm of a product.

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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), allowing the simplification of the logarithm of a quotient.

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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), allowing the simplification of the logarithm of a power.

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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, use properties of logarithms, and isolate the variable.