Logarithm with Base Positive Fraction (Exponent as Negative Mixed Number) Worksheets

Logarithm with Base Positive Fraction (Exponent as Negative Mixed Number) Worksheets

Challenge your students to master advanced logarithmic concepts with these “Logarithm with Base Positive Fraction (Exponent as Negative Mixed Number)” worksheets! Tailored for Grades 9–12, this resource focuses on logarithmic and exponential expressions where the base is a positive fraction (between 0 and 1) and the exponent is a negative mixed number, combining the principles of reciprocals, roots, and fractional powers in one comprehensive practice set.
Students will learn how to convert between logarithmic and exponential forms, apply laws of exponents and logarithms, and interpret results that involve decay and reciprocal relationships. Each worksheet provides step-by-step examples, guided problem sets, and challenging exercises designed to strengthen both procedural fluency and conceptual understanding.
Key Features:
• Focus on logarithms with fractional bases (0 < base < 1) and negative mixed-number exponents
• Reinforces reciprocal, root, and decay concepts in exponential relationships
• Step-by-step worked examples and progressive exercises
• Strengthens understanding of logarithmic and exponential connections
• Ideal for Grades 9–12 | PDF printable | Complete answer key included
Perfect for: Algebra II, Precalculus, or advanced exponential and logarithmic function lessons — great for classroom instruction, individual practice, or exam review.

Worksheets are made in 8.5” x 11” Standard Letter Size. This resource is helpful in students’ assessment, Independent Studies, group activities, practice and homework. This product is available in PDF format and ready to print as well. AI is used in some parts of the product, where deemed necessary.