Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Exponentials & LogarithmsYear 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — Answers
logₐ y = x means ax = y. Log laws: log a + log b = log ab; log a − log b = log (a ÷ b); log aⁿ = n log a.
1.Solve: 32x − 2 = 9
Answer: x = 2
- 9 = 32
- 2x − 2 = 2
- x = 2
2.Solve: 32x − 2 = 729
Answer: x = 4
- 729 = 36
- 2x − 2 = 6
- x = 4
3.Write as a single logarithm: log 7 + log 2
Answer: log 14
log a + log b = log ab
4.Write as a single logarithm: log 30 − log 5
Answer: log 6
log a − log b = log (a ÷ b)
5.Evaluate log₁₀ .
Answer: -1
10-1 =
6.Write as a single logarithm: log 9 + log 7
Answer: log 63
log a + log b = log ab
7.Evaluate log₃ 3.
Answer: 1
31 = 3
8.Evaluate log₂ 128.
Answer: 7
27 = 128
9.Solve: 23x = 64
Answer: x = 2
- 64 = 26
- 3x = 6
- x = 2
10.Write as a single logarithm: log 24 − log 6
Answer: log 4
log a − log b = log (a ÷ b)
11.Solve: 2x − 3 = 2
Answer: x = 4
- 2 = 21
- x − 3 = 1
- x = 4
12.Write as a single logarithm: log 9 − log 3
Answer: log 3
log a − log b = log (a ÷ b)
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