Year 12 Logarithms and Exponential Equations Worksheet — Level 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 — 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.Solve: 102x = 1000000
Answer: x = 3
- 1000000 = 106
- 2x = 6
- x = 3
2.Write as a single logarithm: log 7 + log 3
Answer: log 21
log a + log b = log ab
3.Evaluate log₁₀ 1000.
Answer: 3
103 = 1000
4.Solve: 22x − 2 = 4
Answer: x = 2
- 4 = 22
- 2x − 2 = 2
- x = 2
5.Evaluate log₅ 1.
Answer: 0
50 = 1
6.Write as a single logarithm: log 2 + log 6
Answer: log 12
log a + log b = log ab
7.Write as a single logarithm: log 16 − log 4
Answer: log 4
log a − log b = log (a ÷ b)
8.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
9.Evaluate log₁₀ 100.
Answer: 2
102 = 100
10.Evaluate log₅ 125.
Answer: 3
53 = 125
11.Write as a single logarithm: log 36 − log 9
Answer: log 4
log a − log b = log (a ÷ b)
12.Write as a single logarithm: log 12 − log 6
Answer: log 2
log a − log b = log (a ÷ b)
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