6.5.1 Solving equations with exponentials and logarithms Quiz: Pearson Edexcel Maths, Unit 6

The 20 questions

1. What is the correct first step to solve 3^(2x) = 15 by taking natural logs?

   • ln(3^(2x)) = ln(15)
   • 2x ln(3) = 15
   • ln(3^(2x)) = 15
   • 3 ln(2x) = ln(15)

2. Solve 2^x = 7, giving x to 3 significant figures.

   • 0.845
   • 2.81
   • 3.50
   • 1.95

3. Which law of logarithms is used to simplify log(a) + log(b)?

   • Addition law
   • Power law
   • Division law
   • Multiplication law

4. Simplify the expression log(x^3) using logarithm laws.

   • log(3x)
   • 3 log(x)
   • (log x)^3
   • 3 + log(x)

5. Solve e^(3x) = 20 for exact x.

   • ln(20)/3
   • 3 ln(20)
   • ln(20/3)
   • ln(60)

6. What is the inverse function of f(x) = e^x?

   • 1/e^x
   • log_10(x)
   • e^(-x)
   • ln(x)

7. Solve ln(2x - 1) = 3 for x in exact form.

   • (e^3 + 1)/2
   • e^(1.5)
   • e^3 / 2
   • (e^3 - 1)/2

8. Which base does the 'ln' function use?

   • 10
   • e
   • 2
   • 1

9. Solve the equation 5^(x-1) = 12 giving x to 3 significant figures.

   • 3.54
   • 2.49
   • 2.54
   • 1.54

10. What is the value of ln(e^4)?

    • 1
    • e
    • 4
    • e^4

11. Solve log_2(x) + log_2(3) = 4 for x.

    • 6
    • 16/3
    • 13/3
    • 32

12. Solve 3^x = 2^(x+1) by taking logarithms.

    • ln(2) / ln(3)
    • ln(3) / ln(2)
    • ln(6) / ln(2)
    • ln(2) / ln(1.5)

13. Solve the quadratic-form exponential equation e^(2x) - 5e^x + 6 = 0 for e^x.

    • 2 and 3
    • 1 and 6
    • -2 and -3
    • e^2 and e^3

14. Using the substitution y = e^x, solve e^(2x) - 5e^x + 6 = 0 for x.

    • ln(2) and ln(3)
    • 2 and 3
    • e^2 and e^3
    • ln(5) and ln(6)

15. Solve log_3(x) - 2 log_3(2) = 1 for x.

    • 3
    • 7
    • 12
    • 18

16. What is the exact solution to 4^x = 8^(x-1)?

    • 6
    • 1.5
    • 2
    • 3

17. Solve ln(x) + ln(x - 3) = ln(4) for positive x.

    • -1
    • 4 and -1
    • 1
    • 4

18. What is the solution to 10^x = 50?

    • log_10(50)
    • ln(50)
    • 5
    • 10^5

19. Solve e^x - 12e^(-x) = 1 by using a substitution.

    • ln(3)
    • ln(4)
    • 4
    • ln(12)

20. Evaluate log_5(1) without a calculator.

    • Undefined
    • 0
    • 1
    • 5

Related quizzes

• Exponential function e^x and its graph Quiz · 6.1.1 · 20 questions
• Exponential functions e^kx and their gradients Quiz · 6.2.1 · 20 questions
• Logarithms and the definition of log_a x Quiz · 6.3.1 · 20 questions
• Laws of logarithms Quiz · 6.4.1 · 20 questions
• Logarithmic graphs and estimating parameters Quiz · 6.6.1 · 20 questions
• Exponential growth and decay Quiz · 6.7.1 · 20 questions
• Structure of mathematical proof and methods of proof Quiz · 1.1.1 · 20 questions
• Vectors in two and three dimensions Quiz · 10.1.1 · 20 questions
• Laws of indices for all rational exponents Quiz · 2.1.1 · 20 questions
• Straight lines and their equations Quiz · 3.1.1 · 20 questions