Practice Logarithms

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log_b(x) = y ↔ bʸ = x

  • log₂(8) = 3 because 2³ = 8
  • log₁₀(100) = 2 because 10² = 100
Worked Examples
Example 1
📊 Logarithms - Logarithm definition:
Calculate:

\(\log_{2}(8) = ?\)
Explanation:
📊 Logarithm definition
The rule:
\(\log_a(b) = x \Leftrightarrow a^x = b\)
① Expression:
\(\log_{2}(8)\)
② Ask: what power of 2 gives 8?
\(8 = 2^{3}\)
③ Substitute into the logarithm:
\(\log_{2}(2^{3})\)
④ Apply the rule:
\(\log_{2}(8) = 3\)
✓ Answer: \(3\)
Example 2
📊 Logarithms - Logarithm definition:
Calculate:

\(\log(100) = ?\)
Explanation:
📊 Logarithm definition
The rule:
\(\log_a(b) = x \Leftrightarrow a^x = b\)
① Expression:
\(\log(100)\)
② Ask: what power of 10 gives 100?
\(100 = 10^{2}\)
③ Substitute into the logarithm:
\(\log(10^{2})\)
④ Apply the rule:
\(\log(100) = 2\)
✓ Answer: \(2\)
Example 3
📊 Logarithms - Logarithm definition:
Calculate:

\(\log_{3}(27) = ?\)
Explanation:
📊 Logarithm definition
The rule:
\(\log_a(b) = x \Leftrightarrow a^x = b\)
① Expression:
\(\log_{3}(27)\)
② Ask: what power of 3 gives 27?
\(27 = 3^{3}\)
③ Substitute into the logarithm:
\(\log_{3}(3^{3})\)
④ Apply the rule:
\(\log_{3}(27) = 3\)
✓ Answer: \(3\)
Practice

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