Logarithm with Base Positive Fraction (Exponent as Negative Integer) Worksheets

Logarithm with Base Positive Fraction (Exponent as Negative Integer) Worksheets

Deepen students’ understanding of logarithmic and exponential relationships with these “Logarithm with Base Positive Fraction (Exponent as Negative Integer)” worksheets! Ideal for Grades 9–12, this resource focuses on logarithmic expressions where the base is a positive fraction (between 0 and 1) and the exponent is a negative integer, helping learners grasp how negative powers and fractional bases interact in exponential decay.
Students will practice rewriting logarithmic and exponential forms, applying laws of exponents and logarithms, and interpreting results involving reciprocals and inverse relationships. Each worksheet provides step-by-step examples, guided practice, and challenging problems that promote both procedural fluency and conceptual depth.
Key Features:
• Focus on logarithms with fractional bases (0 < base < 1) and negative integer exponents
• Reinforces reciprocal and decay concepts in exponential relationships
• Includes guided examples and progressive practice problems
• Strengthens understanding of exponent and logarithm connections
• Ideal for Grades 9–12 | PDF printable | Complete answer key included
Perfect for: Algebra II, Precalculus, or advanced logarithmic and exponential function units — excellent for classroom activities, homework, or exam preparation.

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.