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

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

Challenge your students’ understanding of exponents and logarithms with these “Logarithm with Base Positive Fraction Numbers (Exponent as Negative Mixed Number)” worksheets! Designed for Grades 9–12, this advanced resource helps learners explore logarithmic relationships where the base is a positive fraction (between 0 and 1) and the exponent is a negative mixed number, combining concepts of fractional powers, reciprocals, and exponential decay.

Students will practice converting between exponential and logarithmic forms, simplifying expressions, and applying the laws of exponents and logarithms to solve problems with precision. Each worksheet includes guided examples, step-by-step practice problems, and conceptual reasoning questions to build both understanding and confidence in handling complex rational and mixed-number exponents.

Key Features:
Focus on logarithmic equations with fractional bases (0 < base < 1) and negative mixed-number exponents
Reinforces concepts of reciprocal powers and exponential decay
Includes worked examples and progressively challenging exercises
Builds fluency in simplifying and interpreting logarithmic expressions
Excellent for upper-level algebra and precalculus learners
Ideal for Grades 9–12 | PDF printable | Complete answer key included

Perfect for: Advanced Algebra and Precalculus classes, exponential and logarithmic function practice, classwork, homework, and 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.