What is the power rule for logarithms?

The power rule states that $$\text{log}_b(x^k) = k \times \text{log}_b(x)$$ .

How do you solve the equation $$\text{log}_2(x + 3) = 4$$ ?

To solve $$\text{log}_2(x + 3) = 4$$ , convert to exponential form: $$x + 3 = 2^4$$ , which simplifies to $$x + 3 = 16$$ , so $$x = 13$$ .

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

The value of $$\text{log}_e(e)$$ is 1, because any logarithm of its base equals 1.

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

The value of $$\text{ln}(1)$$ is 0, because $$e^0 = 1$$ .

How do you solve for $$y$$ in the equation $$\text{ln}(y + 3) = w$$ ?

To solve for $$y$$ , exponentiate both sides: $$y + 3 = e^w$$ , then $$y = e^w - 3$$ .

What is the base of the common logarithm?

The base of the common logarithm is 10, denoted as $$\text{log}(x)$$ or $$\text{log}_{10}(x)$$ .

What is the relationship between $$\text{log}_b(x)$$ and $$\text{log}_{1/b}(x)$$ ?

The relationship is $$\text{log}_{1/b}(x) = -\text{log}_b(x)$$ .

What is the value of $$\text{log}_3(9)$$ ?

The value of $$\text{log}_3(9)$$ is 2, because $$3^2 = 9$$ .

3.4-3.5 Recap (Solving equations with Logs) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the relationship between logarithms and exponents?

Back

3.

FLASHCARD QUESTION

Front

What is the natural logarithm?

Back

4.

FLASHCARD QUESTION

Front

How do you convert from logarithmic form to exponential form?

Back

5.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

6.

FLASHCARD QUESTION

Front

What is the product rule for logarithms?

Back

7.

FLASHCARD QUESTION

Front

What is the quotient rule for logarithms?

Back

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