Solving Logarithmic Equations
Authored by David Buchanan
Mathematics
11th - 12th Grade
CCSS covered
Used 7K+ times
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About
This quiz focuses on solving logarithmic equations, covering the fundamental techniques students need to master this essential topic in advanced algebra and pre-calculus. The questions assess grade 11-12 level skills, progressing from basic logarithm properties through complex equation-solving strategies. Students must demonstrate mastery of the product property of logarithms (log a + log b = log ab), the ability to convert between logarithmic and exponential forms, techniques for solving equations with logarithms of equal bases, and recognition of extraneous solutions that may arise during the solving process. The problems require students to apply the one-to-one property of logarithmic functions, manipulate algebraic expressions within logarithmic arguments, and understand the relationship between natural logarithms and the mathematical constant e. Success on this quiz demands solid algebraic manipulation skills, understanding of domain restrictions for logarithmic functions, and the ability to check solutions for validity within the original equation's constraints. Created by David Buchanan, a Mathematics teacher in the US who teaches grades 11 and 12. This quiz serves as an excellent tool for formative assessment during a logarithmic equations unit, allowing teachers to identify specific areas where students need additional support before moving to more complex exponential and logarithmic applications. The variety of problem types makes it ideal for homework assignments that reinforce classroom instruction, warm-up activities that activate prior knowledge of logarithm properties, or review sessions before unit tests. Teachers can use individual questions for targeted practice on specific solving techniques, while the complete quiz provides comprehensive coverage of the topic. The mix of computational problems and conceptual understanding questions aligns with Common Core standards A-REI.4 (solving equations in one variable) and F-BF.5 (understanding the inverse relationship between exponents and logarithms), supporting students' development of procedural fluency alongside conceptual understanding of logarithmic relationships.
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15 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Solve log(x) + log(x+3) = 1
Tags
CCSS.HSF.BF.B.5
CCSS.HSA.REI.A.1
CCSS.HSA.CED.A.1
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
log2(x + 2) + log2x = 3
Tags
CCSS.HSF.BF.B.5
CCSS.HSA.REI.A.1
CCSS.HSA.CED.A.1
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
log5(4x-7)=log5(x+5)
Tags
CCSS.HSF.BF.B.5
CCSS.HSA.REI.A.1
CCSS.HSA.REI.B.3
CCSS.HSF.LE.A.4
4.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Solve
Tags
CCSS.HSA.REI.A.1
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Tags
CCSS.HSF.BF.B.5
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
log4(3x-1)=log4(2x+3)
4
3
1
8
Tags
CCSS.HSF.BF.B.5
CCSS.HSA.CED.A.1
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