Year 10 Logarithms and Exponential Equations Worksheet — Level 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 — 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 log₅ 625.
Answer: 4
54 = 625
2.Write as a single logarithm: log 81 − log 9
Answer: log 9
log a − log b = log (a ÷ b)
3.Evaluate log₂ 128.
Answer: 7
27 = 128
4.Write as a single logarithm: log 24 − log 8
Answer: log 3
log a − log b = log (a ÷ b)
5.Write as a single logarithm: log 6 + log 6
Answer: log 36
log a + log b = log ab
6.Solve: 103x = 1000000
Answer: x = 2
- 1000000 = 106
- 3x = 6
- x = 2
7.Solve: 5x + 3 = 5
Answer: x = −2
- 5 = 51
- x + 3 = 1
- x = −2
8.Write as a single logarithm: log 4 − log 2
Answer: log 2
log a − log b = log (a ÷ b)
9.Evaluate log₁₀ 100.
Answer: 2
102 = 100
10.Evaluate log₁₀ .
Answer: -1
10-1 =
11.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
12.Solve: 32x = 81
Answer: x = 2
- 81 = 34
- 2x = 4
- x = 2
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