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Value of Logarithmic Expression

CAT 2017 Slot 1 · Quantitative Ability · Medium · Exponents and Logarithms

This is a medium Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Exponents and Logarithms. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The value of log⁡0.0085+log⁡381−7\log_{0.008} \sqrt{5} + \log_{\sqrt{3}} 81 - 7 is equal to:

  1. A.

    13\frac{1}{3}

  2. B.

    23\frac{2}{3}

  3. C.

    56\frac{5}{6}

  4. D.

    76\frac{7}{6}

Answer

C

Explanation

0.008=5−30.008 = 5^{-3} and 5=51/2\sqrt{5} = 5^{1/2}, so log⁡0.0085=1/2−3=−16\log_{0.008} \sqrt{5} = \frac{1/2}{-3} = -\frac{1}{6}. 3=31/2\sqrt{3} = 3^{1/2} and 81=3481 = 3^4, so log⁡381=41/2=8\log_{\sqrt{3}} 81 = \frac{4}{1/2} = 8. Expression =−16+8−7=1−16=56= -\frac{1}{6} + 8 - 7 = 1 - \frac{1}{6} = \frac{5}{6}.

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