Year 13 Logarithms and Exponential Equations Worksheet — Level 2 — Practice Set 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 2 — Practice Set 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.Evaluate log₁₀ 10000.
Answer: 4
104 = 10000
2.Evaluate log₅ 125.
Answer: 3
53 = 125
3.Evaluate log₃ 27.
Answer: 3
33 = 27
4.Write 54 = 625 in logarithm form.
Answer: log₅ 625 = 4
ax = y means logₐ y = x.
5.Write as a single logarithm: log 8 − log 2
Answer: log 4
log a − log b = log (a ÷ b)
6.Write 3-1 = in logarithm form.
Answer: log₃ = -1
ax = y means logₐ y = x.
7.Write as a single logarithm: log 18 − log 3
Answer: log 6
log a − log b = log (a ÷ b)
8.Evaluate log₂ 64.
Answer: 6
26 = 64
9.Evaluate log₁₀ 10.
Answer: 1
101 = 10
10.Evaluate log₅ 5.
Answer: 1
51 = 5
11.Evaluate log₁₀ 1000.
Answer: 3
103 = 1000
12.Write as a single logarithm: log 7 + log 9
Answer: log 63
log a + log b = log ab
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