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JAMB 1987 · UME · Q14

Simplify without using tables log⁡26−log⁡23log⁡28−2log⁡212\dfrac{\log_2 6 - \log_2 3}{\log_2 8 - 2\log_2 \frac12}.

Worked solution (try it first)
  1. Top: subtracting logs divides, so log⁡26−log⁡23=log⁡22=1\log_2 6 - \log_2 3 = \log_2 2 = 1.
  2. Bottom: log⁡28=3\log_2 8 = 3 and log⁡212=−1\log_2 \frac12 = -1, so the bottom is 3−2(−1)3 - 2(-1), which is 3+2=53 + 2 = 5.
  3. So the value is 15\frac15, option A.

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