2³ × 2⁴ equals 2⁷ and (3²)³ equals 3⁶, so this IB sheet opens by combining exponents, then turns to logarithms with logₐ x + logₐ y as the product rule. Simple logarithm answers of 3 and 2 follow in the key.
Key Takeaways
2³ × 2⁴ = 2⁷ (Q1).
(3²)³ = 3⁶ (Q2).
Q6 records logₐ x + logₐ y as a logarithm law.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.2³ × 2⁴ is equal to
(a) 2⁷(b) 2¹²(c) 4⁷(d) 2¹
2.(3²)³ is equal to
(a) 3⁶(b) 3⁵(c) 3⁸(d) 9³
3.The value of 2⁰ is
(a) 1(b) 0(c) 2(d) undefined
4.log₂ 8 is equal to
(a) 3(b) 2(c) 4(d) 8
5.log₁₀ 100 is equal to
(a) 2(b) 1(c) 10(d) 100
6.The logarithm rule for a product states that logₐ (xy) =
(a) logₐ x + logₐ y(b) logₐ x − logₐ y(c) logₐ x × logₐ y(d) x logₐ y
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State the law of indices for multiplying powers with the same base.
8.Evaluate 2⁵.
9.Write log₂ 16 = 4 in exponential form.
10.Evaluate log₃ 27.
11.State the logarithm law for logₐ (x ÷ y).
12.What is the value of logₐ 1 for any positive base a?
13.Write the change of base formula.
14.Express 2³ = 8 in logarithmic form.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Using logₐ (xy) = logₐ x + logₐ y, simplify log₁₀ 4 + log₁₀ 25.
16.Solve log₁₀ x = 3 for x.
17.Solve 2ˣ = 16 for x.
18.Using the power law, simplify 3 log₁₀ 2.
19.Solve log₂ x = 5 for x.
20.Using the change of base formula log₁₀ 8 ÷ log₁₀ 2, evaluate log₂ 8.
Answer Key
1. a) 2⁷
2. a) 3⁶
3. a) 1
4. a) 3
5. a) 2
6. a) logₐ x + logₐ y
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is 2³ × 2⁴?
2⁷, option (a) in this worksheet (Q1).
What is (3²)³?
3⁶, option (a) in this worksheet (Q2).
What is logₐ x + logₐ y?
logₐ(xy), option (a) in this worksheet (Q6).
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