The equation xlog3⁡x2−(9/2)log3⁡x+5=33 has

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at least one real solution

exactly three real solutions

exactly one irrational solution

complex roots

answer is A.

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Detailed Solution

Given equation isxlog3⁡x2−(9/2)log3⁡x+5=33or xlog3⁡x2−(9/2)log3⁡x+5=33/2or log3⁡x2−(9/2)log3⁡x+5log3⁡x=32----iPut log3 X =tThen from Eq. (i),t3−92t2+5t=32or 2t3−9t2+10t−3=0or (t−1)2t2−7t+3=0or (t−1)t−12(t−3)=0∴t=12,1,3or log3⁡x=12,1,3⇒x=3,3,27.

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