Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 4 — 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 4 — 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 9 + log 7
Answer: log 63
log a + log b = log ab
2.Write as a single logarithm: log 15 − log 3
Answer: log 5
log a − log b = log (a ÷ b)
3.Write as a single logarithm: log 45 − log 5
Answer: log 9
log a − log b = log (a ÷ b)
4.Write as a single logarithm: log 6 + log 8
Answer: log 48
log a + log b = log ab
5.Evaluate log₁₀ 1000.
Answer: 3
103 = 1000
6.Solve: 33x = 729
Answer: x = 2
- 729 = 36
- 3x = 6
- x = 2
7.Write as a single logarithm: log 48 − log 8
Answer: log 6
log a − log b = log (a ÷ b)
8.Write as a single logarithm: log 14 − log 2
Answer: log 7
log a − log b = log (a ÷ b)
9.Evaluate log₂ .
Answer: -1
2-1 =
10.Solve: 3x + 5 = 3
Answer: x = −4
- 3 = 31
- x + 5 = 1
- x = −4
11.Evaluate log₁₀ .
Answer: -2
10-2 =
12.Write as a single logarithm: log 12 − log 3
Answer: log 4
log a − log b = log (a ÷ b)
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