If `log_(9^(1/2))x+log_(9^(1/3))x+. . .` upto 21 terms = 504 . Find x

log_(x)(9x^(2))*log_(3)^(2)(x)=4

If for x,y in R , x gt 0 , y=log_(10)x+log_(10)x^(1//3)+log_(10)x^(1//9)+ ...........upto oo terms and (2+4+6+........+2y)/(3+6+9+.......+3y)=(4)/(log_(10)x) , then the ordered pair (x,y) is equal to :

log_(x)(log_(9)(3^(x)-9))<1

If (1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n terms") = (20)/(7 " log"_(10)x) and n = log_(10)x + log_(10) x^((1)/(2)) + log_(10) x^((1)/(4)) + log_(10) x^((1)/(8)) + ... + oo , then x is equal to

If y=log_(10)x+log_(10)x^(1/3)+log_(10)x^(1/9)+ . . . and (2+4+6+ . . . +2y)/(3+6+9+ . . . +3y)=4/log_(10) x then find the value of x and y

log_(3)(log_(9)x+(1)/(2)+9^(x))=2x

log_(3)(log_(9)x+(1)/(2)+9^(x))=2x

If sum of the first 21 terms of series log _((1)/( 9 ^(2))) x + log _((1)/(9 ^(3))) x + log _((1)/( 9 ^(4))) x + ..., where x gt 0 is 504, then x is equal to :

log_(3) (log_(9)x + 1/2 + 9^(x)) = 2x