Year 13 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 13 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Exponentials & LogarithmsYear 13 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 63 − log 7
Answer: log 9
log a − log b = log (a ÷ b)
2.Evaluate log₂ 128.
Answer: 7
27 = 128
3.Write as a single logarithm: log 9 + log 6
Answer: log 54
log a + log b = log ab
4.Write as a single logarithm: log 6 + log 9
Answer: log 54
log a + log b = log ab
5.Evaluate log₂ 16.
Answer: 4
24 = 16
6.Evaluate log₃ 27.
Answer: 3
33 = 27
7.Evaluate log₁₀ 100.
Answer: 2
102 = 100
8.Solve: 23x + 3 = 8
Answer: x = 0
- 8 = 23
- 3x + 3 = 3
- x = 0
9.Write as a single logarithm: log 5 + log 6
Answer: log 30
log a + log b = log ab
10.Solve: 102x + 6 = 10000
Answer: x = −1
- 10000 = 104
- 2x + 6 = 4
- x = −1
11.Evaluate log₁₀ 1.
Answer: 0
100 = 1
12.Evaluate log₅ 25.
Answer: 2
52 = 25
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