>I gave the precal students, my students for AP Calculus next year, a Calculus readness test and one of the problems is log2(x+1)=8-log2(x-1). The answer that I get is Plus or minus 3, but the right answer, I believe is sqrt(6562). I need someone to explain why the >answer is the latter and not +-3. Since b^x = b^y yields x=y. > > > > Before making any changes to the equation, think about the set of numbers that can go in the "x" position and make statements (either true or false) about real numbers. Because the domain of the base 2 log function, that set of real numbers must be those greater than 1. This must be kept in mind when you replace this equation with one that you consider more convenient, such as log2(x^2-1)=8. This new, more convenient equation has two solutions, the square roots of 257. However, the original equation has only the positive square root as a solution.