CAT Practice : Exponents and Logarithms

Simple inequalities questions appear exponentially tougher when Logarithms are thrown in.

Logarithm - Inequalities

    Q.5: < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b.
    1. 214
    2. 216
    3. 200
    4. 203

 

  • Correct Answer
    Choice A. 214

Explanatory Answer

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Detailed Solution

< 0
log3x = y
< 0
y ∈ (3, 5)
3 < log3x < 5
27 < x < 243
Therefore max ( a – b) will be when a = 242 and b = 28. Therefore, max(a – b) = 214.
Answer choice (A)

Correct Answer: 214



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