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.Solve: 3x + 3 = 27
Answer: x = 0
- 27 = 33
- x + 3 = 3
- x = 0
2.Write as a single logarithm: log 7 + log 8
Answer: log 56
log a + log b = log ab
3.Write as a single logarithm: log 5 + log 8
Answer: log 40
log a + log b = log ab
4.Write as a single logarithm: log 10 − log 5
Answer: log 2
log a − log b = log (a ÷ b)
5.Write as a single logarithm: log 9 + log 5
Answer: log 45
log a + log b = log ab
6.Solve: 10x − 1 = 100
Answer: x = 3
- 100 = 102
- x − 1 = 2
- x = 3
7.Solve: 22x − 2 = 64
Answer: x = 4
- 64 = 26
- 2x − 2 = 6
- x = 4
8.Write as a single logarithm: log 24 − log 3
Answer: log 8
log a − log b = log (a ÷ b)
9.Solve: 23x + 3 = 512
Answer: x = 2
- 512 = 29
- 3x + 3 = 9
- x = 2
10.Evaluate log₅ .
Answer: -1
5-1 =
11.Write as a single logarithm: log 2 + log 7
Answer: log 14
log a + log b = log ab
12.Solve: 53x = 15625
Answer: x = 2
- 15625 = 56
- 3x = 6
- x = 2
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