Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 12 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Exponentials & LogarithmsYear 12 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.Write as a single logarithm: log 4 + log 8
Answer: log 32
log a + log b = log ab
2.Evaluate log₅ .
Answer: -1
5-1 =
3.Evaluate log₂ 4.
Answer: 2
22 = 4
4.Evaluate log₂ 2.
Answer: 1
21 = 2
5.Write as a single logarithm: log 40 − log 8
Answer: log 5
log a − log b = log (a ÷ b)
6.Solve: 33x = 19683
Answer: x = 3
- 19683 = 39
- 3x = 9
- x = 3
7.Write as a single logarithm: log 3 + log 3
Answer: log 9
log a + log b = log ab
8.Solve: 52x + 4 = 625
Answer: x = 0
- 625 = 54
- 2x + 4 = 4
- x = 0
9.Evaluate log₁₀ .
Answer: -1
10-1 =
10.Evaluate log₅ 1.
Answer: 0
50 = 1
11.Write as a single logarithm: log 3 + log 9
Answer: log 27
log a + log b = log ab
12.Write as a single logarithm: log 4 + log 3
Answer: log 12
log a + log b = log ab
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