Your equations should cover each of the following topics: Solving a polynomial inequality of degree 6 or more, that will involve using the Rational Zero Theorem and two other types of factoring. Solving an exponential equation that involves two powers with different bases, not convertible to the common base. Solving a logarithmic equation that involves two logarithms and a constant, and uses law(s) of logarithms and the change of base formula to arrive at the final solution. Solving a trigonometric equation that involves at least two trigonometric ratios and uses restrictions and at least one identity to arrive at the final solution.