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Column-I
Column-II
\( \mathrm{P} \)
(A) Given \( x1 \) and \( \log _{x}\left(x^{x^{2}}\right)+\log _{x}\left(x^{-5 x}\right)=\log _{x}\left(\frac{1}{x^{6}}\right) \).
(P) 2
The sum of all values of \( x \) that satisfying the equation, is
(B) Let \( 0x\pi, 3^{\tan x}=27^{\sin x} \), then the value of \( \sec x \), is
(Q) 3
(C) Let \( a=x-2 \) and \( b=x-4 \).
The value of \( x \) satisfying the equation
(R) 4
\( \frac{\log _{a}(x-3) \log _{b}(x+10)}{\log _{b}(x-3)}=2 \), is
(S) 5
(D) The real values of \( x \) so that all terms are real and
(T) 6 satisfy the equation \( \sqrt{2 \mathrm{x}}=\sqrt{\mathrm{x}+7}-1 \), is
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