Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Exponentials & LogarithmsYear 11 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.Solve: 102x + 6 = 10000
Answer: x = −1
- 10000 = 104
- 2x + 6 = 4
- x = −1
3.Evaluate log₁₀ 1.
Answer: 0
100 = 1
4.Solve: 3x − 1 = 9
Answer: x = 3
- 9 = 32
- x − 1 = 2
- x = 3
5.Solve: 5x + 3 = 5
Answer: x = −2
- 5 = 51
- x + 3 = 1
- x = −2
6.Write as a single logarithm: log 6 + log 8
Answer: log 48
log a + log b = log ab
7.Solve: 2x + 4 = 8
Answer: x = −1
- 8 = 23
- x + 4 = 3
- x = −1
8.Write as a single logarithm: log 9 + log 5
Answer: log 45
log a + log b = log ab
9.Solve: 22x + 6 = 16
Answer: x = −1
- 16 = 24
- 2x + 6 = 4
- x = −1
10.Write as a single logarithm: log 2 + log 8
Answer: log 16
log a + log b = log ab
11.Evaluate log₅ .
Answer: -2
5-2 =
12.Evaluate log₃ 3.
Answer: 1
31 = 3
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