Laws of logarithms

Laws of logarithms Quiz

Spec 5.2 · Edexcel International A Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Simplify log⁡a6−log⁡a2\log_a6-\log_a2.

    • A. log⁡a4\log_a4
    • B. log⁡a3\log_a3
    • C. log⁡a12\log_a12
    • D. log⁡a6log⁡a2\frac{\log_a6}{\log_a2}

  2. 2. Which is equal to 3log⁡a23\log_a2?

    • A. log⁡a6\log_a6
    • B. log⁡a9\log_a9
    • C. log⁡a8\log_a8
    • D. log⁡a5\log_a5

  3. 3. Given log⁡ax=4\log_ax=4, find log⁡a(1x)\log_a\left(\frac1x\right).

    • A. 44
    • B. −4-4
    • C. 14\frac14
    • D. −14-\frac14

  4. 4. Find log⁡aa5−log⁡aa\log_aa^5-\log_aa.

    • A. 55
    • B. 66
    • C. 11
    • D. 44

  5. 5. Which statement is true for all positive xx and yy?

    • A. log⁡a(x+y)=log⁡ax+log⁡ay\log_a(x+y)=\log_ax+\log_ay
    • B. log⁡axy=log⁡ax−log⁡ay\log_a\frac xy=\log_ax-\log_ay
    • C. log⁡ax2=(log⁡ax)2\log_a x^2=\left(\log_ax\right)^2
    • D. log⁡axlog⁡ay=log⁡axy\frac{\log_ax}{\log_ay}=\log_a\frac xy

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