The number of integral value of x satisfying the equation 
− 
= 2
Text Solution
Verified by ExpertsA
– 
= 2 ⇒ |2log 3 x – 2| – |log 3 x – 2| = 2
case Ι If log 3 x – 2 ≥ 0 ⇒ log 3 x ≥ 2
Then 2 log 3 x – 2 – log 3 x + 2 = 2 ⇒ log 3 x = 2
∴ log 3 x = 2 ⇒ x = 3 2 = 9 ⇒ x = 9
case ΙΙ 1 ≤ log 3 x < 2
∴ 2 log 3 x – 2 + log 3 x – 2 = 2 ⇒ 3 log 3 x = 6 ⇒ log 3 x = 2
which is not possible
case ΙΙΙ If log 3 x < 1 the – 2 log 3 x + 2 + log 3 x – 2 = 2
– log 3 x = 2 ⇒ log 3 x = – 2
∴ x = 3 –2 = 
⇒ x = 9, 
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