Exponential Equations and Properties
6 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the value of x in the equation $2^x=16$?

4

What is the result of $(2^3)^x$?

2^{3x}

What expression simplifies to -1(3x-7) in the equation $(5^{-1})^{3x-7}$?

5^{-3x+7}

What does $(4^{-3})^{1-x^3}$ simplify to?

<p>-3(1-x^2) = 4^{-3 + 3x^2}</p> Signup and view all the answers

For the equation $2^{x-3}=64$, what is the value of x?

<p>6</p> Signup and view all the answers

What is the final value of x in the equation derived from $2^{x-3}=64$?

<p>9</p> Signup and view all the answers

Study Notes

Exponential Equations

  • Solve (2^x = 16) to find (x = 4) since (16) can be expressed as (2^4).

Exponent Properties

  • Using properties of exponents, ((2^3)^x) simplifies to (2^{3x}).

Negative Exponents

  • The expression ((5^{-1})^{3x - 7}) simplifies as follows:
    • First, apply exponent rules to get (5^{-(3x - 7)}).
    • This leads to the equation (-1(3x - 7) = 5^{-3x + 7}).

Manipulation of Negative Exponents

  • ((4^{-3})^{1 - x^3}) can be manipulated:
    • Transforms to (-3(1 - x^2) = 4^{-3 + 3x^2}).

Solving Variations of Exponential Equations

  • For (2^{x-3} = 64):
    • Recognize that (64 = 2^6) to set the equation as (2^6 = 2^{x^2 - 3}).
    • This gives (6 = x^2 - 3).
    • By adding (3) to both sides, (9 = x^2), which leads to (x = 3) or (x = -3) (considering square roots).

Practice Critical Thinking

  • Review methods used for transforming and solving various exponential equations for a comprehensive understanding.

Understanding Exponential Rules

  • Ensure strong grasp of properties of exponents, including multiplication, division, and power rules, which are essential for simplifying expressions.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Description

This quiz covers various concepts related to exponential equations, including solving simple exponential equations and understanding the properties of exponents. You will also explore manipulations involving negative exponents and apply critical thinking to solve different variations of exponential equations. Test your knowledge and enhance your skills in handling exponential functions.

More Like This

Use Quizgecko on...
Browser
Browser