What is the horizontal asymptote of the function $$f(x) = 2 \times 3^{(x+1)} - 4$$ ?

The horizontal asymptote is $$y = -4$$ .

What is the equivalent exponential equation for $$\text{ln}(50) = x$$ ?

The equivalent exponential equation is $$e^x = 50$$ .

What is the value of $$\text{log}_3(27)$$ ?

The value is 3, since $$3^3 = 27$$ .

What does it mean for a function to have a horizontal asymptote?

A function has a horizontal asymptote if it approaches a specific value as $$x$$ approaches infinity or negative infinity.

What is the formula for converting from logarithmic to exponential form?

The formula is: If $$\text{log}_b(a) = c$$ , then $$b^c = a$$ .

What is the value of $$\text{ln}(e)$$ ?

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

What is the significance of the base in a logarithm?

The base determines the rate at which the logarithmic function grows. For example, base 10 logarithms grow slower than base 2 logarithms.

What is the vertical asymptote of the function $$f(x) = \frac{1}{x}$$ ?

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

How do you find the horizontal asymptote of a rational function?

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator.

What is the definition of an exponential function?

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is the base, and $$x$$ is the exponent.

ExLog Test Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an Asymptote?

Back

2.

FLASHCARD QUESTION

Front

Rewrite the exponential equation 3^4 = 81 in logarithmic form.

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

6.

FLASHCARD QUESTION

Front

What is the base of the natural logarithm?

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between exponential and logarithmic functions?

Back

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