Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 4 — 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 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.Evaluate log₂ .
Answer: -2
2-2 =
2.Write as a single logarithm: log 6 + log 7
Answer: log 42
log a + log b = log ab
3.Write as a single logarithm: log 4 + log 6
Answer: log 24
log a + log b = log ab
4.Evaluate log₂ .
Answer: -1
2-1 =
5.Evaluate log₅ 625.
Answer: 4
54 = 625
6.Evaluate log₃ 1.
Answer: 0
30 = 1
7.Write as a single logarithm: log 2 + log 4
Answer: log 8
log a + log b = log ab
8.Evaluate log₅ 1.
Answer: 0
50 = 1
9.Evaluate log₂ 32.
Answer: 5
25 = 32
10.Evaluate log₁₀ 100.
Answer: 2
102 = 100
11.Solve: 23x = 8
Answer: x = 1
- 8 = 23
- 3x = 3
- x = 1
12.Solve: 5x + 1 = 125
Answer: x = 2
- 125 = 53
- x + 1 = 3
- x = 2
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