Year 11 Logarithms and Exponential Equations Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Exponentials & LogarithmsYear 11 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.Solve: 5x + 3 = 25
Answer: x = −1
- 25 = 52
- x + 3 = 2
- x = −1
2.Write as a single logarithm: log 40 − log 8
Answer: log 5
log a − log b = log (a ÷ b)
3.Solve: 33x = 19683
Answer: x = 3
- 19683 = 39
- 3x = 9
- x = 3
4.Solve: 53x = 1953125
Answer: x = 3
- 1953125 = 59
- 3x = 9
- x = 3
5.Write as a single logarithm: log 4 + log 2
Answer: log 8
log a + log b = log ab
6.Solve: 53x + 6 = 125
Answer: x = −1
- 125 = 53
- 3x + 6 = 3
- x = −1
7.Write as a single logarithm: log 20 − log 5
Answer: log 4
log a − log b = log (a ÷ b)
8.Evaluate log₅ 125.
Answer: 3
53 = 125
9.Solve: 23x + 6 = 8
Answer: x = −1
- 8 = 23
- 3x + 6 = 3
- x = −1
10.Write as a single logarithm: log 9 − log 3
Answer: log 3
log a − log b = log (a ÷ b)
11.Solve: 52x + 2 = 25
Answer: x = 0
- 25 = 52
- 2x + 2 = 2
- x = 0
12.Write as a single logarithm: log 2 + log 8
Answer: log 16
log a + log b = log ab
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