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MathematicsSS 1en

📊 Indices and Laws of Logarithms

This quiz covers the fundamental principles of indices and logarithms, essential tools for solving exponential and power-based equations in advanced mathematics. **What you'll learn:** - Simplify expressions using the laws of indices (product, quotient, power rules) - Convert between exponential and logarithmic form - Apply logarithm laws to solve equations and simplify complex expressions - Evaluate logarithms with different bases and verify identities - Solve real-world problems involving exponential growth and decay

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Questions in this quiz

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  1. Question 1

    Simplify 23×252^3 \times 2^5 using the laws of indices.

  2. Question 2

    log⁡5(25)=2\log_5(25) = 2 because 52=255^2 = 25.

  3. Question 3

    If 3x=813^x = 81, then x=x = ___

  4. Question 4

    log⁡a(xy)=log⁡a(x)+log⁡a(y)\log_a(xy) = \log_a(x) + \log_a(y) for all positive values of aa, xx and yy where a≠1a \neq 1.

  5. Question 5

    Simplify (a3)2×a−4a2\frac{(a^3)^2 \times a^{-4}}{a^2} using the laws of indices.

  6. Question 6

    Express log⁡3(27)−log⁡3(9)\log_3(27) - \log_3(9) as a single logarithm: \log_3 \left(\frac{___}{___}\right)

  7. Question 7

    If log⁡2(x)=5\log_2(x) = 5, what is the value of xx?

  8. Question 8

    log⁡a(b)=log⁡c(b)log⁡c(a)\log_a(b) = \frac{\log_c(b)}{\log_c(a)} (change of base formula) is valid for any bases aa and cc where a,c>0a, c > 0 and a,c≠1a, c \neq 1.

  9. Question 9

    Solve 2x−1=82^{x-1} = 8 for xx.

  10. Question 10

    Simplify log⁡5(125)+log⁡5(25)−log⁡5(5)\log_5(125) + \log_5(25) - \log_5(5) to a single value.