Grade 12 Logarithmic Expansion Worksheet
This worksheet focuses on expanding logarithmic expressions using the properties of logarithms, suitable for Grade 12 mathematics.
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Logarithmic Expansion Practice
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Expand each logarithmic expression completely using the properties of logarithms. Assume all variables are positive.
1. Expand: log₃(xy)
2. Expand: log₂(x/y)
3. Expand: log₅(x³)
4. Expand: ln(x²y⁵)
5. The expansion of log(a²b/c³) is .
6. The expansion of ln(√(x⁵y)) is .
7. The expansion of log₄((x+1)² / (y-2)) is .
8. Which of the following is the correct expansion of log(x³/y⁴)?
3log(x) + 4log(y)
3log(x) - 4log(y)
log(x³) / log(y⁴)
log(3x) - log(4y)
9. The expression ln(e²x) expands to:
2ln(x)
2 + ln(x)
e²ln(x)
ln(2) + ln(x)
10. True or False: log(A/B) = log(A) - log(B)
True
False
11. True or False: log(A+B) = log(A) + log(B)
True
False
12. Expand log₃( (x²y³) / (z√w) ) completely.
13. Expand ln( (e⁵x⁴) / (y²z) ) completely.