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 2 + log 2
Answer: log 4
log a + log b = log ab
2.Solve: 32x + 2 = 729
Answer: x = 2
- 729 = 36
- 2x + 2 = 6
- x = 2
3.Evaluate log₅ .
Answer: -2
5-2 =
4.Evaluate log₅ .
Answer: -1
5-1 =
5.Solve: 33x − 3 = 19683
Answer: x = 4
- 19683 = 39
- 3x − 3 = 9
- x = 4
6.Solve: 2x + 4 = 4
Answer: x = −2
- 4 = 22
- x + 4 = 2
- x = −2
7.Solve: 10x + 5 = 10
Answer: x = −4
- 10 = 101
- x + 5 = 1
- x = −4
8.Write as a single logarithm: log 30 − log 5
Answer: log 6
log a − log b = log (a ÷ b)
9.Solve: 23x − 3 = 64
Answer: x = 3
- 64 = 26
- 3x − 3 = 6
- x = 3
10.Write as a single logarithm: log 8 + log 9
Answer: log 72
log a + log b = log ab
11.Evaluate log₃ 81.
Answer: 4
34 = 81
12.Write as a single logarithm: log 18 − log 6
Answer: log 3
log a − log b = log (a ÷ b)
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