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.Evaluate log₁₀ 1.
Answer: 0
100 = 1
2.Evaluate log₂ 16.
Answer: 4
24 = 16
3.Write as a single logarithm: log 48 − log 8
Answer: log 6
log a − log b = log (a ÷ b)
4.Evaluate log₂ .
Answer: -2
2-2 =
5.Solve: 3x + 4 = 27
Answer: x = −1
- 27 = 33
- x + 4 = 3
- x = −1
6.Write as a single logarithm: log 24 − log 3
Answer: log 8
log a − log b = log (a ÷ b)
7.Solve: 2x = 2
Answer: x = 1
- 2 = 21
- x = 1
- x = 1
8.Evaluate log₁₀ 100.
Answer: 2
102 = 100
9.Write as a single logarithm: log 2 + log 3
Answer: log 6
log a + log b = log ab
10.Write as a single logarithm: log 6 + log 8
Answer: log 48
log a + log b = log ab
11.Solve: 32x + 4 = 81
Answer: x = 0
- 81 = 34
- 2x + 4 = 4
- x = 0
12.Write as a single logarithm: log 4 + log 5
Answer: log 20
log a + log b = log ab
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