MBApyq

Logarithmic Sum Evaluation

XAT 2014 · Quantitative Ability & Data Interpretation · Easy · Algebra

All XAT 2014 questionsMore Algebra questionsAll XAT QADI

The value of the expression: ∑i=21001log⁡i100!\sum_{i=2}^{100} \frac{1}{\log_i 100!} is:

  1. A.

    0.01

  2. B.

    0.1

  3. C.

    1

  4. D.

    10

  5. E.

    100

Answer

C

Explanation

Using change of base formula, 1log⁡i100!=log⁡100!i\frac{1}{\log_i 100!} = \log_{100!} i. Sum =∑i=2100log⁡100!i=log⁡100!(2×3×⋯×100)=log⁡100!(100!)=1= \sum_{i=2}^{100} \log_{100!} i = \log_{100!}(2 \times 3 \times \dots \times 100) = \log_{100!}(100!) = 1.

Related Algebra questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace