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 48 − log 6
Answer: log 8
log a − log b = log (a ÷ b)
2.Solve: 103x + 6 = 1000000
Answer: x = 0
- 1000000 = 106
- 3x + 6 = 6
- x = 0
3.Solve: 10x + 6 = 1000
Answer: x = −3
- 1000 = 103
- x + 6 = 3
- x = −3
4.Write as a single logarithm: log 9 + log 7
Answer: log 63
log a + log b = log ab
5.Write as a single logarithm: log 30 − log 5
Answer: log 6
log a − log b = log (a ÷ b)
6.Write as a single logarithm: log 56 − log 8
Answer: log 7
log a − log b = log (a ÷ b)
7.Solve: 52x + 4 = 25
Answer: x = −1
- 25 = 52
- 2x + 4 = 2
- x = −1
8.Write as a single logarithm: log 6 + log 2
Answer: log 12
log a + log b = log ab
9.Evaluate log₂ 16.
Answer: 4
24 = 16
10.Write as a single logarithm: log 8 + log 5
Answer: log 40
log a + log b = log ab
11.Write as a single logarithm: log 7 + log 5
Answer: log 35
log a + log b = log ab
12.Solve: 103x = 1000000000
Answer: x = 3
- 1000000000 = 109
- 3x = 9
- x = 3
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