Solve This challenging change of Base Logarithmic Equation (Log to Quadratic)|Math Short!
The core problem solved is a logarithmic equation that transforms into the quadratic equation 2p2+3p−2=0, leading to solutions x=2 and x=1/16 Struggling with complex logarithmic equations? Learn the step-by-step method to solve a log equation by converting it into a quadratic equation! In this math short, we tackle a problem where the base of the logarithm needs adjustment to simplify the equation. Step-by-Step Solution Highlights: Change of Base: We first simplify the equation by using the relationship logba1=logab. Substitution: We introduce a substitution (p=logx4) to transform the equation into a solvable quadratic form: p1−p=23. Quadratic Solution: We solve the resulting quadratic equation 2p2+3p−2=0 by factorization to find the values for p. Final Solution: We substitute back to find the final values for x, which are x=2 and x=1/16. This is a common type of problem found in Algebra II, Pre-Calculus, and College-level Mathematics exams. Master this technique for your next test! #maths #logarithms #logarithmicfunctions #algebra #precalculus #mathproblems #mathshorts #joeeducate # quadratics, high school math
