Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — 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 — 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.Write as a single logarithm: log 12 − log 6
Answer: log 2
log a − log b = log (a ÷ b)
2.Evaluate log₅ 125.
Answer: 3
53 = 125
3.Evaluate log₂ 32.
Answer: 5
25 = 32
4.Write as a single logarithm: log 6 − log 3
Answer: log 2
log a − log b = log (a ÷ b)
5.Evaluate log₃ .
Answer: -2
3-2 =
6.Write as a single logarithm: log 10 − log 5
Answer: log 2
log a − log b = log (a ÷ b)
7.Solve: 22x + 4 = 16
Answer: x = 0
- 16 = 24
- 2x + 4 = 4
- x = 0
8.Solve: 5x − 2 = 25
Answer: x = 4
- 25 = 52
- x − 2 = 2
- x = 4
9.Write as a single logarithm: log 30 − log 5
Answer: log 6
log a − log b = log (a ÷ b)
10.Write as a single logarithm: log 3 + log 3
Answer: log 9
log a + log b = log ab
11.Solve: 5x = 25
Answer: x = 2
- 25 = 52
- x = 2
- x = 2
12.Evaluate log₂ .
Answer: -1
2-1 =
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