What does the equation $$y = \text{log}_3(x + 5)$$ represent in terms of transformations?

It represents a horizontal shift of the graph of $$y = \text{log}_3(x)$$ to the left by 5 units.

What is the inverse of the logarithmic function $$f(x) = \text{log}_3(x)$$ ?

The inverse is $$f^{-1}(x) = 3^x$$ .

How do you rewrite the exponential equation $$3^4 = 81$$ in logarithmic form?

In logarithmic form, it is written as $$\text{log}_3(81) = 4$$ .

What is the range of the function $$y = \text{log}_b(x)$$ ?

The range is all real numbers, or $$(-\text{∞}, \text{∞})$$ .

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, denoted as $$b$$ in $$y = \text{log}_b(x)$$ .

What does the graph of $$y = \text{log}_4(x)$$ look like?

The graph passes through the point (1,0), approaches the vertical line $$x=0$$ , and increases without bound as $$x$$ increases.

What is the relationship between logarithmic and exponential functions?

Logarithmic functions are the inverses of exponential functions.

How do you find the x-intercept of the function $$y = \text{log}_3(x)$$ ?

The x-intercept occurs when $$y = 0$$ , which is at $$x = 1$$ .

What is the vertical asymptote of the function $$y = \text{log}_b(x)$$ ?

The vertical asymptote is the line $$x = 0$$ .

What is the value of $$\text{log}_b(b)$$ ?

The value is 1, since $$b^1 = b$$ .

What is the product rule for logarithms?

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

What is the quotient rule for logarithms?

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

Flashcard 10 - Logarithmic Functions Flashcards

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1.

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What is the parent function of logarithmic functions?

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3.

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4.

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5.

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This represents a horizontal shift to the right by 1 unit and a vertical shift up by 4 units.

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