Year 12 Logarithms and Exponential Equations Worksheet — Level 2 — Practice Set 3 — 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 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 log₂ 64.
Answer: 6
26 = 64
2.Write as a single logarithm: log 9 − log 3
Answer: log 3
log a − log b = log (a ÷ b)
3.Write 26 = 64 in logarithm form.
Answer: log₂ 64 = 6
ax = y means logₐ y = x.
4.Write 103 = 1000 in logarithm form.
Answer: log₁₀ 1000 = 3
ax = y means logₐ y = x.
5.Evaluate log₁₀ 10.
Answer: 1
101 = 10
6.Write 10-2 = in logarithm form.
Answer: log₁₀ = -2
ax = y means logₐ y = x.
7.Evaluate log₅ 1.
Answer: 0
50 = 1
8.Write 27 = 128 in logarithm form.
Answer: log₂ 128 = 7
ax = y means logₐ y = x.
9.Write 22 = 4 in logarithm form.
Answer: log₂ 4 = 2
ax = y means logₐ y = x.
10.Write 54 = 625 in logarithm form.
Answer: log₅ 625 = 4
ax = y means logₐ y = x.
11.Write as a single logarithm: log 5 + log 6
Answer: log 30
log a + log b = log ab
12.Evaluate log₃ .
Answer: -2
3-2 =
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