Show that `log_3 sqrt(3 sqrt(3 (sqrt(3.....oo)))=1.`

log9sqrt(3sqrt(3)sqrt(3))=?

log_(9)sqrt(3sqrt(3sqrt(3)))=

log_3 (sqrt sqrt sqrt sqrt(3))

log_9sqrt3sqrt3sqrt3 =

Calculate the value of 2(sqrt(3+sqrt(3+sqrt(3+)))...oo)

The value of log sqrt(2sqrt(2sqrt(2...oo" times")))+log sqrt(3sqrt(3sqrt(3...oo" times"))) is

If y = sqrt(3^x+sqrt(3^x+sqrt(3^x+….......oo))) , then prove that : (2y-1)dy/dx = 3^x log3 .

Prove that (log3sqrt(3)+log sqrt(8)-log sqrt(125))/(log6-log5)=(3)/(2)

log_((4)/(3))(56+(sqrt(56+sqrt(56+sqrt(56+......oo))))/(sqrt(64sqrt(64sqrt(64.....oo)))))

Evaluate : (a) sqrt(xsqrt(xsqrt(x.....oo))) (b) sqrt(6+ sqrt(6 + sqrt(6 + ......oo))) (c) sqrt(a^(3)root(3)(b sqrt(a^(3) root(3)(b.......oo))))