Year 10 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — 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 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 log₂ .
Answer: -1
2-1 =
2.Write as a single logarithm: log 18 − log 6
Answer: log 3
log a − log b = log (a ÷ b)
3.Solve: 102x + 6 = 1000000
Answer: x = 0
- 1000000 = 106
- 2x + 6 = 6
- x = 0
4.Write as a single logarithm: log 3 + log 7
Answer: log 21
log a + log b = log ab
5.Evaluate log₅ 125.
Answer: 3
53 = 125
6.Write as a single logarithm: log 12 − log 6
Answer: log 2
log a − log b = log (a ÷ b)
7.Solve: 103x = 1000000000
Answer: x = 3
- 1000000000 = 109
- 3x = 9
- x = 3
8.Solve: 22x + 2 = 64
Answer: x = 2
- 64 = 26
- 2x + 2 = 6
- x = 2
9.Write as a single logarithm: log 6 + log 7
Answer: log 42
log a + log b = log ab
10.Write as a single logarithm: log 4 − log 2
Answer: log 2
log a − log b = log (a ÷ b)
11.Write as a single logarithm: log 9 + log 7
Answer: log 63
log a + log b = log ab
12.Solve: 3x + 6 = 27
Answer: x = −3
- 27 = 33
- x + 6 = 3
- x = −3
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