Logarithms I — O/L Mathematics

How do I practise Logarithms I?

2 questions with worked solutions

1. Convert the logarithmic equation log₃(81) = 4 into its equivalent index (exponential) form.
   1. A) 3⁴ = 81
   2. B) 4³ = 81
   3. C) 81³ = 4
   4. D) 3 × 4 = 81
   Check my answer

   Correct answer: A) 3⁴ = 81

   By definition of logarithm: log_b(a) = c is equivalent to base^c = a. Here, base is 3, power is 4, and number is 81: 3⁴ = 81.

   Show worked solution

   Step 1: Identify base, argument, and exponent in log₃(81) = 4: Base = 3, Exponent = 4, Value = 81. Step 2: Express in power form: Base^Exponent = Value. Step 3: 3⁴ = 81. Answer: 3⁴ = 81.
   Modelled on: the O/L Mathematics examination pattern
2. Find the value of x if log₂ x = 5.
   1. A) 32
   2. B) 10
   3. C) 25
   4. D) 7
   Check my answer

   Correct answer: A) 32

   A logarithm is an index: log₂ x = 5 says that 2 raised to the power 5 gives x. So x = 2⁵ = 32.

   Show worked solution

   Step 1: Identify the parts of log₂ x = 5: base = 2, index = 5, value = x. Step 2: Write in index form: x = 2⁵. Step 3: Evaluate: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Answer: x = 32.
   Modelled on: the O/L Mathematics examination pattern

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Where does Logarithms I fit in the syllabus?

Grade 10 · Term 2