What is the domain of a logarithmic function?

The domain of a logarithmic function is the set of positive real numbers, as logarithms are undefined for zero and negative numbers.

What is the product rule for logarithms?

The product rule states that $$\text{log}_b(mn) = \text{log}_b(m) + \text{log}_b(n)$$ .

What is the quotient rule for logarithms?

The quotient rule states that $$\text{log}_bigg(\frac{m}{n}igg) = \text{log}_b(m) - \text{log}_b(n)$$ .

What is the power rule for logarithms?

The power rule states that $$\text{log}_b(m^p) = p \times \text{log}_b(m)$$ .

If $$\text{log}_b(x) = y$$ , what is the equivalent exponential form?

The equivalent exponential form is $$b^y = x$$ .

What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a given value. In $$\text{log}_b(x)$$ , $$b$$ is the base.

What is the significance of the natural logarithm?

The natural logarithm, denoted as $$\text{ln}(x)$$ , uses the base $$e$$ (approximately 2.718) and is widely used in calculus and mathematical modeling.

FLASHCARD on Solving Exponential and Logarithmic Equations Flashcards

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FLASHCARD QUESTION

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What is the definition of a logarithm?

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