Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — 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 2 — 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 log₁₀ 1.
Answer: 0
100 = 1
2.Write as a single logarithm: log 2 + log 9
Answer: log 18
log a + log b = log ab
3.Solve: 103x + 6 = 1000
Answer: x = −1
- 1000 = 103
- 3x + 6 = 3
- x = −1
4.Write as a single logarithm: log 4 − log 2
Answer: log 2
log a − log b = log (a ÷ b)
5.Write as a single logarithm: log 6 − log 3
Answer: log 2
log a − log b = log (a ÷ b)
6.Write as a single logarithm: log 9 + log 2
Answer: log 18
log a + log b = log ab
7.Solve: 53x + 6 = 15625
Answer: x = 0
- 15625 = 56
- 3x + 6 = 6
- x = 0
8.Evaluate log₅ 625.
Answer: 4
54 = 625
9.Evaluate log₃ 3.
Answer: 1
31 = 3
10.Solve: 32x − 2 = 729
Answer: x = 4
- 729 = 36
- 2x − 2 = 6
- x = 4
11.Evaluate log₅ 5.
Answer: 1
51 = 5
12.Evaluate log₅ 25.
Answer: 2
52 = 25
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