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JAMB 2015 · UTME · Q28

Given that log⁡a2=0.693\log_a 2 = 0.693 and log⁡a3=1.097\log_a 3 = 1.097, find log⁡a13.5\log_a 13.5.

Worked solution (try it first)
  1. Write 13.5 using 2 and 3: 13.5=272=33213.5 = \frac{27}{2} = \frac{3^3}{2}.
  2. So log⁡a13.5=3log⁡a3−log⁡a2\log_a 13.5 = 3\log_a 3 - \log_a 2.
  3. That is 3(1.097)−0.693=3.291−0.693=2.5983(1.097) - 0.693 = 3.291 - 0.693 = 2.598, option C.

Also set as JAMB 1997 · UME · Q4

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