Year 13 Logarithms and Exponential Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 13 exponentials & logarithms worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Exponentials & LogarithmsYear 13 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.Write as a single logarithm: log 20 − log 5
Answer: log 4
log a − log b = log (a ÷ b)
2.Write as a single logarithm: log 6 − log 3
Answer: log 2
log a − log b = log (a ÷ b)
3.Solve: 53x = 1953125
Answer: x = 3
- 1953125 = 59
- 3x = 9
- x = 3
4.Solve: 23x + 3 = 8
Answer: x = 0
- 8 = 23
- 3x + 3 = 3
- x = 0
5.Write as a single logarithm: log 2 + log 4
Answer: log 8
log a + log b = log ab
6.Write as a single logarithm: log 12 − log 3
Answer: log 4
log a − log b = log (a ÷ b)
7.Evaluate log₂ .
Answer: -1
2-1 =
8.Write as a single logarithm: log 63 − log 7
Answer: log 9
log a − log b = log (a ÷ b)
9.Solve: 23x − 3 = 8
Answer: x = 2
- 8 = 23
- 3x − 3 = 3
- x = 2
10.Solve: 32x + 6 = 81
Answer: x = −1
- 81 = 34
- 2x + 6 = 4
- x = −1
11.Evaluate log₃ .
Answer: -2
3-2 =
12.Solve: 102x = 100
Answer: x = 1
- 100 = 102
- 2x = 2
- x = 1
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