Year 11 Logarithms and Exponential Equations Worksheet — Level 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 — 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 log₅ .
Answer: -1
5-1 =
2.Solve: 10x − 3 = 1000
Answer: x = 6
- 1000 = 103
- x − 3 = 3
- x = 6
3.Solve: 5x + 2 = 5
Answer: x = −1
- 5 = 51
- x + 2 = 1
- x = −1
4.Write as a single logarithm: log 5 + log 6
Answer: log 30
log a + log b = log ab
5.Solve: 32x + 4 = 9
Answer: x = −1
- 9 = 32
- 2x + 4 = 2
- x = −1
6.Solve: 52x + 2 = 15625
Answer: x = 2
- 15625 = 56
- 2x + 2 = 6
- x = 2
7.Evaluate log₃ .
Answer: -2
3-2 =
8.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
9.Write as a single logarithm: log 28 − log 4
Answer: log 7
log a − log b = log (a ÷ b)
10.Solve: 52x = 625
Answer: x = 2
- 625 = 54
- 2x = 4
- x = 2
11.Solve: 3x − 3 = 3
Answer: x = 4
- 3 = 31
- x − 3 = 1
- x = 4
12.Evaluate log₂ 4.
Answer: 2
22 = 4
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