Logarithmic Expansion Worksheet
Expand logarithmic expressions using the properties of logarithms.
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Logarithmic Expansion Worksheet
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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) )