Logarithmic Expansion Worksheet
Expand logarithmic expressions using the properties of logarithms.
Includes
Standards
Topics
Logarithmic Expansion Worksheet
Name:
Date:
Score:
Expand each logarithmic expression completely using the properties of logarithms. Assume all variables are positive.
1. Expand: log₃(xy²)
2. Expand: ln(x³/y)
3. Expand: log(√(x/z))
4. The product rule for logarithms states that logₐ(MN) = .
5. The quotient rule for logarithms states that logₐ(M/N) = .
6. The power rule for logarithms states that logₐ(Mᵖ) = .
7. Which of the following is the correct expansion of log₅(a³b)?
3 log₅a + log₅b
log₅(3a) + log₅b
log₅a + 3 log₅b
3(log₅a + log₅b)
8. The expression log(x²/y³) can be expanded as:
2logx - 3logy
3logx - 2logy
log(x²) / log(y³)
log(x/y)⁶
9. The expression log₄(x + y) can be expanded to log₄x + log₄y.
True
False
10. log₇(x/y) = log₇x - log₇y is an example of the quotient rule for logarithms.
True
False
11. Expand completely: log₅( (x²y) / z³ )
12. Expand completely: ln( (e⁴x) / (yz²) )
Related Worksheets
Logarithm Rules Practice Worksheet
Practice applying the fundamental rules of logarithms, including product, quotient, power, and change of base rules.
Logarithmic Equations Worksheet
Solve and understand logarithmic equations with this comprehensive worksheet for Grade 9 students.
Logarithmic Modeling Worksheet
Explore logarithmic functions and their applications in modeling real-world phenomena at a Grade 9 level.
Natural Logarithm Worksheet
This worksheet focuses on understanding and applying the natural logarithm (ln) for Grade 9 students.
Change of Base Formula Worksheet
Understand and apply the change of base formula for logarithms with this Grade 9 math worksheet.
Logarithmic to Exponential Conversion Worksheet
Practice converting logarithmic equations to their equivalent exponential form for Grade 9 Math students.
Logarithmic Properties Worksheet
A Grade 9 math worksheet focusing on the properties of logarithms, including product, quotient, and power rules.
Logarithm Word Problems Worksheet
Solve real-world problems using logarithms, including growth, decay, and Richter scale applications.