GATE 2023 ST – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Let a=30!,b=50!,c=100!. Which inequality is correct?

log_c a < log_b a < log_a b < log_a c
log_c a < log_a b < log_b a < log_b c
log_c a < log_b a < log_a c < log_a b
log_b a < log_c a < log_a b < log_a c

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Show answer and explanation

Correct answer: (A) log_c a < log_b a < log_a b < log_a c

Explanation

Since 1<a<b<c, their natural logs obey 0<ln a<ln b<ln c. Therefore ln a/ln c<ln a/ln b<1<ln b/ln a<ln c/ln a. Convert each ratio by change of base to obtain **A**.

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