Can You Solve This in 10 Seconds? (99% Fail)

Can you solve for x in the exponential equation 3^(x² - 6) = 1/81? This problem often stumps students who panic when they see a quadratic in the exponent. However, there's a quick and elegant trick that makes the solution incredibly simple. In this video, we walk you through the key insight: expressing both sides of the equation with a common base (base 3). By recognizing that 81 is 3^4, we can rewrite 1/81 as 3^-4. Once the bases match, we can equate the exponents and solve the simple resulting quadratic equation. We show the full step-by-step process and verify the final answer. This is a must-know technique for algebra, pre-calculus, and math competition problems!