CAT Exam Model Paper 3 with solutions for free online practice

Question : 72 of 100

Marks: +1, -0

The value of x satisfying the equation

| x - 1 | ^ { \log _ { 3 } x ^ { 2 } - 2 \log _ { x} 9 } = ( x - 1 ) ^ { 7 }

Solution:

(b) Best way is to go through options.
Consider option (b)

| 3 ^ { 4 } - 1 | ^ { \log _ { 3 } \ ( 3 ^ { 4 } \ ) ^ { 2 } - 2 \log _ { 81 } 9 } = ( 3 ^ { 4 } - 1 ) ^ { 7 }

| 80 | ^ { \log _ { 3 } 3 ^ { 8 } - \log _ { 81 } 81} = ( 80 ) ^ { 7 }

⇒

\log _ { 3 } 3 ^ { 8 } - \log _ { 81 } 81 = 7

⇒7 = 7
Hence option (b) is correct.

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