Year 12 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 12 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Exponentials & LogarithmsYear 12 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.Write as a single logarithm: log 10 − log 5
Answer: log 2
log a − log b = log (a ÷ b)
2.Write as a single logarithm: log 9 + log 4
Answer: log 36
log a + log b = log ab
3.Evaluate log₅ 1.
Answer: 0
50 = 1
4.Solve: 103x − 3 = 1000000
Answer: x = 3
- 1000000 = 106
- 3x − 3 = 6
- x = 3
5.Write as a single logarithm: log 56 − log 7
Answer: log 8
log a − log b = log (a ÷ b)
6.Write as a single logarithm: log 8 + log 8
Answer: log 64
log a + log b = log ab
7.Evaluate log₃ 1.
Answer: 0
30 = 1
8.Solve: 5x + 5 = 125
Answer: x = −2
- 125 = 53
- x + 5 = 3
- x = −2
9.Solve: 5x + 3 = 25
Answer: x = −1
- 25 = 52
- x + 3 = 2
- x = −1
10.Write as a single logarithm: log 4 + log 5
Answer: log 20
log a + log b = log ab
11.Evaluate log₁₀ 10.
Answer: 1
101 = 10
12.Write as a single logarithm: log 6 + log 8
Answer: log 48
log a + log b = log ab
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