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

The value of $$\text{log}_b(b) = 1$$ .

What is the value of $$\text{log}_b(1)$$ ?

The value of $$\text{log}_b(1) = 0$$ for any base $$b > 0$$ .

What is exponential growth?

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, represented by the function $$f(t) = a(1 + r)^t$$ , where $$r$$ is the growth rate.

What is exponential decay?

Exponential decay occurs when a quantity decreases by a fixed percentage over time, represented by the function $$f(t) = a(1 - r)^t$$ , where $$r$$ is the decay rate.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

What is the domain of a logarithmic function?

The domain of a logarithmic function is all positive real numbers, i.e., $$x > 0$$ .

What is the range of a logarithmic function?

The range of a logarithmic function is all real numbers, i.e., $$(-\text{∞}, +\text{∞})$$ .

What is the significance of the point (1, 0) in logarithmic functions?

The point (1, 0) indicates that the logarithm of 1 is always 0, regardless of the base.

How do you convert an exponential equation to a logarithmic equation?

To convert $$b^y = x$$ to logarithmic form, write it as $$y = \text{log}_b(x)$$ .

What is the vertical asymptote of a logarithmic function?

The vertical asymptote of a logarithmic function is the line $$x = 0$$ .

Graphs: Exponential & Logarithmic

Flashcard

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Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-IF.C.7E, HSF.BF.B.5, HSF-BF.B.4A

Standards-aligned

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FLASHCARD QUESTION

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What is an exponential function?

Back

FLASHCARD QUESTION

Front

What is the general form of a logarithmic function?

Back

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