Exponential and logarithmic inequalities

Develop reliable methods for exponential and logarithmic inequalities, including bases between zero and one. This precalculus practice set connects monotonicity, positive logarithm arguments, interval notation and threshold decisions. Tasks move from comparing powers to solving inequalities with nonlinear arguments and substitutions.

You will decide when an inequality keeps its direction, when it reverses, and which algebraic endpoints remain admissible. Compound restrictions and integer-time questions make the difference between a formal boundary and a valid final answer explicit. Single-select and multiselect questions include error diagnosis and justification, so a correct interval must be supported by a valid method.

Prerequisites are exponential and logarithmic equations, logarithm laws, quadratic factoring and basic interval inequalities. Write domain restrictions first and test a value when unsure about direction. Worked explanations show how the original domain, monotonicity and equality conditions fit together. The bank progresses in authored difficulty while remaining independent of delivery order. Use mistakes to distinguish a logarithm-domain gap from an inequality-sign or algebra error, then revisit the corresponding prerequisite before attempting new examples.