Year 10 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 3 — 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 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 + 6 = 10000
Answer: x = −1
- 10000 = 104
- 2x + 6 = 4
- x = −1
2.Solve: 5x − 2 = 25
Answer: x = 4
- 25 = 52
- x − 2 = 2
- x = 4
3.Write as a single logarithm: log 3 + log 9
Answer: log 27
log a + log b = log ab
4.Solve: 10x − 1 = 10
Answer: x = 2
- 10 = 101
- x − 1 = 1
- x = 2
5.Solve: 102x + 4 = 10000
Answer: x = 0
- 10000 = 104
- 2x + 4 = 4
- x = 0
6.Write as a single logarithm: log 9 + log 8
Answer: log 72
log a + log b = log ab
7.Evaluate log₃ .
Answer: -1
3-1 =
8.Solve: 53x − 3 = 1953125
Answer: x = 4
- 1953125 = 59
- 3x − 3 = 9
- x = 4
9.Solve: 103x − 3 = 1000000
Answer: x = 3
- 1000000 = 106
- 3x − 3 = 6
- x = 3
10.Solve: 103x + 6 = 1000000000
Answer: x = 1
- 1000000000 = 109
- 3x + 6 = 9
- x = 1
11.Solve: 2x − 3 = 2
Answer: x = 4
- 2 = 21
- x − 3 = 1
- x = 4
12.Evaluate log₁₀ 1000.
Answer: 3
103 = 1000
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