How do you solve an exponential equation of the form $$a^x = b$$ ?

Take the logarithm of both sides: $$x = \frac{\text{ln}(b)}{\text{ln}(a)}$$ .

How do you express $$4^{2x} = 19$$ in logarithmic form?

You can express it as $$x = \frac{\text{log}_4(19)}{2}$$ .

What is the logarithmic identity for $$\text{ln}(a^b)$$ ?

The identity states that $$\text{ln}(a^b) = b \times \text{ln}(a)$$ .

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

The result is 0, since e^0 = 1.

What is the relationship between exponential and logarithmic functions?

Exponential functions are the inverse of logarithmic functions. If $$y = a^x$$ , then $$x = \text{log}_a(y)$$ .

What is the property of logarithms that allows you to combine the logarithm of a product?

The property states that $$\text{ln}(a \times b) = \text{ln}(a) + \text{ln}(b)$$ .

How do you solve $$e^x = 9$$ for x?

Take the natural logarithm of both sides: $$x = \text{ln}(9)$$ .

What is the solution to the equation $$4^{2x} = 19$$ ?

The solution is $$x = \frac{\text{log}_4(19)}{2}$$ .

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

The result is 1, since e^1 = e.

What is the property of exponents that states $$a^{m-n} = \frac{a^m}{a^n}$$ ?

This property allows you to subtract exponents when dividing exponential expressions with the same base.

LT 3c Solving Exponential Equations Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the natural logarithm of a number?

Back

The natural logarithm, denoted as ln, is the logarithm to the base e, where e is approximately equal to 2.71828. It is used to solve equations involving exponential growth.

2.

FLASHCARD QUESTION

Front

What property of logarithms allows you to expand the logarithm of a quotient?

Back

3.

FLASHCARD QUESTION

Front

What happens to exponents when two exponential expressions with the same base are multiplied?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.71828.

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

9 questions

Inequalities

Flashcard

•

9th Grade

11 questions

Climate Change and Its Causes

Flashcard

•

KG

10 questions

Essential Statistics Concepts

Flashcard

•

12th Grade

10 questions

R2.3 How Far? Le Chatelier's Principle

Flashcard

•

12th Grade

10 questions

High Note 2. Unit 1. Test your vocabulary

Flashcard

•

10th Grade

11 questions

Memoriter_1

Flashcard

•

12th Grade

15 questions

Anatomy Review

Flashcard

•

12th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

10 questions

Probability Practice

Quiz

•

4th Grade

15 questions

Probability on Number LIne

Quiz

•

4th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

6 questions

Appropriate Chromebook Usage

Lesson

•

7th Grade

10 questions

Greek Bases tele and phon

Quiz

•

6th - 8th Grade

Discover more resources for Mathematics

23 questions

TSI Math Vocabulary

Quiz

•

10th - 12th Grade

80 questions

ACT Math Important Vocabulary

Quiz

•

11th Grade

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

11 questions

Slopes of Parallel and Perpendicular Lines

Quiz

•

7th - 11th Grade

13 questions

Identify Transformations in Geometry

Quiz

•

8th - 12th Grade

20 questions

Quadratic Transformations Review

Quiz

•

9th - 12th Grade

10 questions

Area of 2D Shapes

Quiz

•

7th - 11th Grade