The set of all `x` satisfying the equation `x^(log)_3x^2+((log)_3x)^(2-10)=1/(x^2)i s` 1 (b) 2 (c) 3 (d) 0

Options

A. `{1, 9}`
B. ` {1, 9, 1//81}`
C. `{1, 4, 1//81}`
D. ` {9, 1//81}`

Answer

D

Explanation

Taking log of both sides with base 3, we have
` (log_(3)x^(2)+(log_(3) x)^(2) - 10)(log_(3)x)=- 2 log_(3) x`
` rArrlog_(3)x = 0 or 2 log_(3) x + (log_(3) x) ^(2) - 8 = 0`
` rArr x = 1, or log_(3) x=2, -4`.
Hence, ` x = 1, 3^(2), 3^(-4)`.