How do you express $$\text{log}_b(m^n)$$ in terms of $$m$$ and $$n$$ ?

Using the Power Rule: $$\text{log}_b(m^n) = n \times \text{log}_b(m)$$ .

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

$$\text{log}_2(8) = 3$$ because $$2^3 = 8$$ .

What does it mean for a function to be exponential?

An exponential function is of the form $$f(x) = ab^x$$ where $$a$$ is a constant, $$b$$ is the base, and $$b > 0$$ .

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

If $$\text{log}_b(a) = c$$ , then it can be rewritten as $$b^c = a$$ .

What is the value of $$\text{log}_{10}(1000)$$ ?

$$\text{log}_{10}(1000) = 3$$ because $$10^3 = 1000$$ .

What is the formula for the decay of a substance over time?

The decay can be modeled by $$N(t) = N_0 e^{-kt}$$ where $$N_0$$ is the initial amount, $$k$$ is the decay constant, and $$t$$ is time.

What is the significance of the base in a logarithmic function?

The base determines the rate of growth or decay; for example, base 2 indicates a doubling effect.

How do you solve for $$x$$ in the equation $$2^x = 16$$ ?

Take the logarithm: $$x = \text{log}_2(16) = 4$$ .

What is the value of $$\text{log}_2\frac{m^4}{n^7}$$ ?

Using the Quotient Rule: $$\text{log}_2\frac{m^4}{n^7} = 4\text{log}_2(m) - 7\text{log}_2(n)$$ .

PC Chapter 3 Mid Review: Exponential & Logarithmic Functions Flashcards

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1.

FLASHCARD QUESTION

Front

What is the property of logarithms that allows you to express the logarithm of a quotient as the difference of logarithms?

Back

2.

FLASHCARD QUESTION

Front

What is the formula for calculating the half-life of a radioactive substance?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the formula for compound interest?

Back

5.

FLASHCARD QUESTION

Front

If a radioactive substance has a half-life of 7 years, how much of the substance remains after 21 years?

Back

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