Algebra - Solve Exponential Equations Using the K Method

Welcome to MatheNatic! In this video, we are solving for a variable using the K method, a useful technique for handling exponential equations. This method is particularly helpful when the same base appears in different terms with varying exponents. We start by examining the given expression and recognizing a pattern. Two of the terms share the same base, but one is raised to twice the power of the other. The third term does not include this base, which is a clear sign that the K method should be applied. To simplify the equation, we introduce a substitution, replacing the repeating base with a single variable. This allows us to rewrite the original problem as a quadratic expression, which can be solved using factorization. By breaking the quadratic expression into two factors, we find two possible values for our substitution. Since we need to solve for the original variable, we substitute back and analyze both possible values. In one case, we find a straightforward solution by rewriting the expression with matching bases. This reveals the correct answer. However, in the other case, we encounter an issue: a positive base raised to any exponent cannot result in a negative value. Because of this, we conclude that there is no solution for that part of the equation. In the end, we determine that there is only one valid solution. Download Math Study Notes at https://payhip.com/MatheNatic Get started with FREE notes on Statistics and Financial Math! Subscribe to MatheNatic for more High School Mathematics Tutorials: https://www.youtube.com/channel/UCBDkt17RbuVyx9U2-UPffXA #MatheNatic