Correct Answer - Option 3 : 3
Concept:
- \(\rm {log_{a}x^b}={blog_{a}x}\)
- \(\rm a^{log_{a}x}=x\)
Calculation:
Given: \(a^{2log_{a}x}-b^{log_{b}x}= 6\)
⇒ \(a^{log_{a}x^{2}}-b^{log_{b}x}=6\) ( ∴ \(\rm {log_{a}x^b}={blog_{a}x}\))
⇒ x2 - x = 6 ( ∴ \(\rm a^{log_{a}x}=x\))
⇒ x2 - x - 6 = 0
⇒ (x - 3)(x + 2) = 0
⇒ x = 3 and x = - 2
But ∵ x > 0 so, x = 3
Hence, option 3 is correct.