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.Evaluate log₃ .
Answer: -2
3-2 =
2.Write as a single logarithm: log 8 − log 4
Answer: log 2
log a − log b = log (a ÷ b)
3.Write as a single logarithm: log 9 + log 3
Answer: log 27
log a + log b = log ab
4.Evaluate log₂ 8.
Answer: 3
23 = 8
5.Solve: 102x = 100
Answer: x = 1
- 100 = 102
- 2x = 2
- x = 1
6.Evaluate log₃ 27.
Answer: 3
33 = 27
7.Solve: 5x + 3 = 25
Answer: x = −1
- 25 = 52
- x + 3 = 2
- x = −1
8.Write as a single logarithm: log 12 − log 2
Answer: log 6
log a − log b = log (a ÷ b)
9.Solve: 52x + 6 = 625
Answer: x = −1
- 625 = 54
- 2x + 6 = 4
- x = −1
10.Write as a single logarithm: log 15 − log 5
Answer: log 3
log a − log b = log (a ÷ b)
11.Evaluate log₂ 4.
Answer: 2
22 = 4
12.Write as a single logarithm: log 64 − log 8
Answer: log 8
log a − log b = log (a ÷ b)
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