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Find the value of x  if \(a^{2log_{a}x}-b^{log_{b}x}= 6\)
1. -2
2. 2
3. 3
4. -3

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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.

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