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JAMB 2017 · UTME · Q35

Find, without using logarithm tables, the value of log⁡327−log⁡1464log⁡1381\dfrac{\log_3 27 - \log_{\frac14} 64}{\log_{\frac13} 81}.

Worked solution (try it first)
  1. 27=3327 = 3^3, so log⁡327=3\log_3 27 = 3.
  2. 64=(14)−364 = \left(\frac14\right)^{-3}, so log⁡1464=−3\log_{\frac14} 64 = -3.
  3. 81=(13)−481 = \left(\frac13\right)^{-4}, so log⁡1381=−4\log_{\frac13} 81 = -4.
  4. The value is 3−(−3)−4=6−4\frac{3 - (-3)}{-4} = \frac{6}{-4}
    =−32= -\frac32, option C.

Also set as JAMB 1984 · UME · Q10

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