What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in $$\text{log}_b(a) = c$$ , $$b$$ is the base.

What is the value of $$\text{log}_2(8)$$ ?

The value of $$\text{log}_2(8)$$ is 3, because $$2^3 = 8$$ .

What is the value of $$\text{log}_{10}(100)$$ ?

The value of $$\text{log}_{10}(100)$$ is 2, because $$10^2 = 100$$ .

How do you solve an exponential equation like $$2^x = 16$$ ?

To solve $$2^x = 16$$ , rewrite 16 as a power of 2: $$2^x = 2^4$$ . Therefore, $$x = 4$$ .

How do you solve a logarithmic equation like $$\text{log}_2(x) = 3$$ ?

To solve $$\text{log}_2(x) = 3$$ , rewrite it in exponential form: $$x = 2^3$$ . Therefore, $$x = 8$$ .

What is the exponential growth formula?

The exponential growth formula is given by $$N(t) = N_0 e^{rt}$$ , where $$N_0$$ is the initial amount, $$r$$ is the growth rate, and $$t$$ is time.

What is the exponential decay formula?

The exponential decay formula is given by $$N(t) = N_0 e^{-rt}$$ , where $$N_0$$ is the initial amount, $$r$$ is the decay rate, and $$t$$ is time.

What is the significance of the number 'e' in exponential functions?

The number 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models. It represents the limit of $$(1 + \frac{1}{n})^n$$ as $$n$$ approaches infinity.

5.2 - 5.3 Flashcard: Graphing/Solving Exponentials & Logs Fall 2024 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential growth?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential decay?

Back

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

How can you identify an exponential growth function from its equation?

Back

5.

FLASHCARD QUESTION

Front

How can you identify an exponential decay function from its equation?

Back

6.

FLASHCARD QUESTION

Front

What is the general form of a logarithmic function?

Back

Tags

CCSS.HSF-IF.C.7E

7.

FLASHCARD QUESTION

Front

What is the relationship between exponential and logarithmic functions?

Back

Tags

CCSS.HSF.BF.B.5

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