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.Write as a single logarithm: log 5 + log 9
Answer: log 45
log a + log b = log ab
2.Evaluate log₂ 64.
Answer: 6
26 = 64
3.Write as a single logarithm: log 30 − log 5
Answer: log 6
log a − log b = log (a ÷ b)
4.Evaluate log₃ 27.
Answer: 3
33 = 27
5.Evaluate log₂ 1.
Answer: 0
20 = 1
6.Evaluate log₃ 81.
Answer: 4
34 = 81
7.Evaluate log₅ 5.
Answer: 1
51 = 5
8.Evaluate log₅ 625.
Answer: 4
54 = 625
9.Solve: 2x + 1 = 8
Answer: x = 2
- 8 = 23
- x + 1 = 3
- x = 2
10.Evaluate log₂ 8.
Answer: 3
23 = 8
11.Solve: 102x + 2 = 100
Answer: x = 0
- 100 = 102
- 2x + 2 = 2
- x = 0
12.Solve: 5x + 5 = 25
Answer: x = −3
- 25 = 52
- x + 5 = 2
- x = −3
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