If `log_(3)2,log_(3)(2^(x)-5)` and `log_(3)(2^(x)-7/2)` are in A.P., then x is equal to

If log_(10)2,log_(10)(2^(x)-1) and log_(10)(2^(x)+3) are in A.P then the value of x is

If log_(2)(5.2^(x)+1),log_(4)(2^(1-x)+1) and 1 are in A.P,then x equals

If log_(2)(5.2^(x)+1),log_(4)(2^(1-x)+1) and 1 are in A.P,then x equals

If 1,log_9(3^(1-x)+2), log_3(4*3^x-1) are in A.P then x equals to

If the reciprocals of 2, log_((3^(x)-4))4 and log_(3^(x)+(7)/(2))4 are in arithmetic progression, then x is equal to

If (log)_3 2,(log)_3(2^x-5) and (log)_3(2^x-7/2) are in arithmetic progression, determine the value of xdot

{:(Column -I,Column -II),((A)"if" 4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1)"then 2x equals",(P)1),((B)"The number of solutions of" log_(7)log_(5)(sqrt(x+5)+sqrt(x))=0 is,(Q)2),((C)"The number of values of x such that the middle term of",(R)3),(log_(2)2 log_(3)(2^(x)-5)log_(3)(2^(x)-(7)/(2))"is the average of the other two is",),((D)"if" alphabeta "are the roots of the equation",(S)4),(x^(2)-(3+2^(sqrt(log_(2)3)-3sqrt(log_(3)2)))x-2(3log_(3)^(2)-2^(log_(2)^(3)))=0,),("then" 2(alpha+beta)-alpha beta"equals",):}

If 2x^(log_(4)3)+3^(log_(4)x)= 27 , then x is equal to

If 1, log_3sqrt(3^(1-x)+2), log_3 (4*3^x-1) are in AP then x equals

If log_(3) sin x-log_(3) cos x-log_(3)(1- tan x)-log_(3)(1+tan x)= -1 , then tan2x is equal to (wherever defined)