Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 12 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Exponentials & LogarithmsYear 12 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 18 − log 6
Answer: log 3
log a − log b = log (a ÷ b)
2.Solve: 3x + 4 = 3
Answer: x = −3
- 3 = 31
- x + 4 = 1
- x = −3
3.Solve: 22x + 6 = 16
Answer: x = −1
- 16 = 24
- 2x + 6 = 4
- x = −1
4.Write as a single logarithm: log 81 − log 9
Answer: log 9
log a − log b = log (a ÷ b)
5.Evaluate log₅ 25.
Answer: 2
52 = 25
6.Write as a single logarithm: log 9 + log 2
Answer: log 18
log a + log b = log ab
7.Write as a single logarithm: log 2 + log 7
Answer: log 14
log a + log b = log ab
8.Evaluate log₁₀ 1000.
Answer: 3
103 = 1000
9.Evaluate log₂ 1.
Answer: 0
20 = 1
10.Evaluate log₅ .
Answer: -1
5-1 =
11.Solve: 10x + 2 = 10
Answer: x = −1
- 10 = 101
- x + 2 = 1
- x = −1
12.Evaluate log₅ .
Answer: -2
5-2 =
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