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.Solve: 32x + 2 = 729
Answer: x = 2
- 729 = 36
- 2x + 2 = 6
- x = 2
2.Evaluate log₁₀ 1.
Answer: 0
100 = 1
3.Solve: 23x = 512
Answer: x = 3
- 512 = 29
- 3x = 9
- x = 3
4.Write as a single logarithm: log 8 + log 2
Answer: log 16
log a + log b = log ab
5.Write as a single logarithm: log 18 − log 3
Answer: log 6
log a − log b = log (a ÷ b)
6.Evaluate log₃ 1.
Answer: 0
30 = 1
7.Evaluate log₃ 27.
Answer: 3
33 = 27
8.Solve: 2x − 1 = 4
Answer: x = 3
- 4 = 22
- x − 1 = 2
- x = 3
9.Evaluate log₅ 125.
Answer: 3
53 = 125
10.Write as a single logarithm: log 6 + log 4
Answer: log 24
log a + log b = log ab
11.Write as a single logarithm: log 5 + log 6
Answer: log 30
log a + log b = log ab
12.Solve: 3x + 2 = 3
Answer: x = −1
- 3 = 31
- x + 2 = 1
- x = −1
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