\Rightarrow 2^x + 3x - 3 = 2^6 - GetMeFoodie
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:
📰 Why Every Style Icon Is Rocking This Black Fur Jacket (You Should Too!) 📰 Tropical Chic? No—This Black Fur Jacket Is the Trend You’re Searching For! 📰 This One Ingredient Transforms Sweet Potato Pie into a Black Soul Food Masterpiece! 📰 Microsoft Drive For Mac 📰 2 The Secret Roth Ira Tax Benefits That Will Change Your Retirement Game 2907088 📰 Fortnite Crashes On Startup 📰 Wells Fargo Phenix City Al 📰 Sony Alpha Ilce6000Lb 3288290 📰 New Netflix Series 9509042 📰 Sign In To Azure 📰 Unlock Excel Secrets The Ultimate Guide To Adding Filters In Seconds 4033267 📰 Discover Why 2300 Oracle Way Austin Tx 78741 Is The Hottest Real Estate Deal In Town 4324508 📰 Credit Cards For Terrible Credit Unsecured 📰 Tactics Ogre Reborn Classes 4902319 📰 Animal Crossing New Horizons Spice Up Your Lifethis Secret Feature Will Blow Your Mind 8061343 📰 Wordle Alternative 8102967 📰 Bollywood News Bollywood 1691060 📰 Roblox Games Unblocked 5400829Final 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:
$$
x = rac{9}{5}
$$
