Year 10 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Exponentials & LogarithmsYear 10 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 log₃ .
Answer: -2
3-2 =
2.Write as a single logarithm: log 8 + log 4
Answer: log 32
log a + log b = log ab
3.Write as a single logarithm: log 12 − log 3
Answer: log 4
log a − log b = log (a ÷ b)
4.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
5.Evaluate log₃ 27.
Answer: 3
33 = 27
6.Evaluate log₁₀ .
Answer: -1
10-1 =
7.Write as a single logarithm: log 16 − log 2
Answer: log 8
log a − log b = log (a ÷ b)
8.Write as a single logarithm: log 40 − log 8
Answer: log 5
log a − log b = log (a ÷ b)
9.Evaluate log₂ 4.
Answer: 2
22 = 4
10.Solve: 103x + 3 = 1000000000
Answer: x = 2
- 1000000000 = 109
- 3x + 3 = 9
- x = 2
11.Write as a single logarithm: log 4 − log 2
Answer: log 2
log a − log b = log (a ÷ b)
12.Write as a single logarithm: log 7 + log 8
Answer: log 56
log a + log b = log ab
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