Year 12 Logarithms and Exponential Equations Worksheet — Level 2 — Practice Set 4 — 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 2 — Practice Set 4 — 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 103 = 1000 in logarithm form.
Answer: log₁₀ 1000 = 3
ax = y means logₐ y = x.
2.Write 31 = 3 in logarithm form.
Answer: log₃ 3 = 1
ax = y means logₐ y = x.
3.Write as a single logarithm: log 54 − log 6
Answer: log 9
log a − log b = log (a ÷ b)
4.Evaluate log₅ 125.
Answer: 3
53 = 125
5.Evaluate log₃ 27.
Answer: 3
33 = 27
6.Write as a single logarithm: log 30 − log 5
Answer: log 6
log a − log b = log (a ÷ b)
7.Write as a single logarithm: log 5 + log 5
Answer: log 25
log a + log b = log ab
8.Write as a single logarithm: log 2 + log 7
Answer: log 14
log a + log b = log ab
9.Write as a single logarithm: log 72 − log 9
Answer: log 8
log a − log b = log (a ÷ b)
10.Evaluate log₂ 2.
Answer: 1
21 = 2
11.Write as a single logarithm: log 30 − log 6
Answer: log 5
log a − log b = log (a ÷ b)
12.Evaluate log₁₀ .
Answer: -2
10-2 =
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