\Rightarrow 2^x + 3x - 3 = 2^6 - Redraw
Solving the Exponential Equation: How to Simplify and Solve namber⁽²ˣ⁺³ˣ⁻³⁾ = 2⁶
Solving the Exponential Equation: How to Simplify and Solve namber⁽²ˣ⁺³ˣ⁻³⁾ = 2⁶
Understanding exponential equations is fundamental in algebra, and equations like ⲹ̽ 2ˣ⁺³ˣ⁻³ ⲹ̽ 2⁶ play a key role in mastering exponents. In this article, we’ll explore how to simplify and solve the equation ⲹ̽ 2⁽²ˣ⁺³ˣ⁻³⁾ = 2⁶ step by step, make sense of the underlying math, and highlight practical tips for solving similar exponential problems.
Understanding the Context
What is the Equation ⲹ̽ 2⁽²ˣ⁺³ˣ⁻³⁾ = 2⁶ All About?
The equation ⲹ̽ 2⁽²ˣ⁺³ˣ⁻³⁾ = 2⁶ is an exponential equation where both sides share the same base — 2. Exponential equations of the form ⲹ̽ aᵘ = aᵇ are easier to solve when the bases are identical because, thanks to exponent rules, the exponents must be equal:
$$
2x + 3x - 3 = 6
$$
This allows us to convert the exponential equation into a simple linear equation in x.
Image Gallery
Key Insights
Step-by-Step Solution
Step 1: Combine like terms on the left side
Simplify the exponent on the left side:
$$
2x + 3x - 3 = 5x - 3
$$
🔗 Related Articles You Might Like:
📰 campari vs aperol 📰 best inexpensive mattress 📰 samantha mathis films 📰 Dont Miss Outcnnq Stocks Are Surging Before Your Eyes 7086913 📰 Popcorn Time Software 9759166 📰 Instapost 7648521 📰 You Wont Believe What Happened When Microsoft Stock Plunged To Xis This A Buying Opportunity 3452545 📰 Butterfly Silhouette 9467115 📰 See These Cute Yet Powerful German Shepherd X Pitbull Hybridsdont Look Away 5766872 📰 Earn Huge Top Marathon Rewards Everyones Craving Right Now 2563294 📰 5 Outrageous How They Outsmarted The Competitionyou Wont Let This Slip Away 7880189 📰 A Factory Produces 500 Units Of A Product In 8 Hours If Production Increases By 25 And Operates For 10 Hours How Many Units Are Produced 2661409 📰 Delayed Sleep Phase Syndrome 1957163 📰 Youll Never Guess What Secret Spy Message Board Revealed In 2025 3516205 📰 Mmo Champion Guide Unlock The Secret To Top Ranked Glory 4416551 📰 This Mac Timer Widget Is Saving Users Minutes Every Daydont Miss Out Try It Now 1389566 📰 How Your Pinch Pleat Curtains Transform Any Room In Seconds 7535080 📰 You Wont Believe What Happened When Vrcaht Formedyoull Shock Your Everyday Life 8593520Final Thoughts
So the equation becomes:
$$
2^{5x - 3} = 2^6
$$
Step 2: Set the exponents equal
Since the bases are equal, we equate the exponents:
$$
5x - 3 = 6
$$
Step 3: Solve for x
Add 3 to both sides:
$$
5x = 9
$$
Divide both sides by 5:
$$
x = rac{9}{5}
$$
