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.Write as a single logarithm: log 18 − log 6
Answer: log 3
log a − log b = log (a ÷ b)
2.Evaluate log₂ 1.
Answer: 0
20 = 1
3.Evaluate log₂ 2.
Answer: 1
21 = 2
4.Evaluate log₃ 9.
Answer: 2
32 = 9
5.Write as a single logarithm: log 12 − log 6
Answer: log 2
log a − log b = log (a ÷ b)
6.Solve: 102x − 2 = 10000
Answer: x = 3
- 10000 = 104
- 2x − 2 = 4
- x = 3
7.Evaluate log₅ 125.
Answer: 3
53 = 125
8.Write as a single logarithm: log 3 + log 5
Answer: log 15
log a + log b = log ab
9.Write as a single logarithm: log 40 − log 8
Answer: log 5
log a − log b = log (a ÷ b)
10.Evaluate log₃ 27.
Answer: 3
33 = 27
11.Solve: 52x = 25
Answer: x = 1
- 25 = 52
- 2x = 2
- x = 1
12.Write as a single logarithm: log 35 − log 7
Answer: log 5
log a − log b = log (a ÷ b)
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