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Find the number of solutions of the equation log₂(x² + 3) = (1/2) * log_(1/3)(x + 1/x) for x > 0.
- 0
- 1
- 2
- infinite
Correct answer: 0
Solution
The LHS = log₂(x²+3) >= log₂(3) > 0 for all x, while the RHS = (1/2)*log_(1/3)(x+1/x) <= 0 for all x > 0 (since x+1/x >= 2 and base 1/3 < 1). LHS > 0 > RHS always, so no solution exists.
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