Math Olympiad | A Beautiful Exponential Equation

Struggling with exponential equations? This Math Olympiad problem is a beautiful test of your algebra fundamentals! We're solving the equation 5^x + 5^x = 40 to find the value of 'x'. While it looks simple, this problem elegantly tests your understanding of combining like terms, isolating exponents, and applying logarithm properties to find the exact solution—all without a calculator, just as you would in a math competition. In this video, I break down the solution into clear, easy-to-follow steps. You'll learn the crucial rules and see how to simplify your answer into its most exact and elegant form. Perfect for students preparing for the SAT, ACT, or any Math Olympiad. Solution Walkthrough: 0:00 Introducing the Problem 0:10 The Crucial First Step (Combining Like Terms) 0:25 Isolating the Exponential Term (5^x) 0:40 Rewriting the Number 20 Strategically 1:20 Applying Exponent Rules 1:30 Using Logarithms to Solve for x 2:30 Writing the Final Answer in Exact Form 2:50 Step-by-Step Verification Key Concepts Covered: Exponential Equations, Logarithm Properties, Power Rule, Change of Base, Math Olympiad Strategies. Explore more at Mathitect. 👉 Subscribe for more tutorials:    / @mathitect   👉 Instagram:   / mathitect   👉 Facebook:   / mathitect   👉 Tiktok:   / mathitect