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JAMB 1984 · UME · Q10

Find without using logarithm tables the value of log⁡327−log⁡1464log⁡3181\dfrac{\log_3 27 - \log_{\frac14} 64}{\log_3 \frac{1}{81}}.

Worked solution (try it first)
  1. 27=3327 = 3^3, so log⁡327=3\log_3 27 = 3.
  2. 64=43=(14)−364 = 4^3 = \left(\frac14\right)^{-3}, so log⁡1464=−3\log_{\frac14} 64 = -3.
  3. 181=3−4\frac{1}{81} = 3^{-4}, so log⁡3181=−4\log_3 \frac{1}{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 2017 · UTME · Q35

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