Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 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 — Practice Set 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 log₃ 9.
Answer: 2
32 = 9
2.Write as a single logarithm: log 18 − log 6
Answer: log 3
log a − log b = log (a ÷ b)
3.Evaluate log₁₀ 1.
Answer: 0
100 = 1
4.Write as a single logarithm: log 15 − log 3
Answer: log 5
log a − log b = log (a ÷ b)
5.Solve: 23x + 6 = 64
Answer: x = 0
- 64 = 26
- 3x + 6 = 6
- x = 0
6.Solve: 3x − 2 = 9
Answer: x = 4
- 9 = 32
- x − 2 = 2
- x = 4
7.Evaluate log₂ 16.
Answer: 4
24 = 16
8.Write as a single logarithm: log 56 − log 8
Answer: log 7
log a − log b = log (a ÷ b)
9.Evaluate log₁₀ .
Answer: -2
10-2 =
10.Write as a single logarithm: log 2 + log 3
Answer: log 6
log a + log b = log ab
11.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
12.Evaluate log₂ 1.
Answer: 0
20 = 1
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