Consider two curves `C_1: y=1/x a n dC_2: y=logx` on the `x y` plane. Let `D_1` denotes the region surrounded by `C_1,C_2,` and the line `x=1a n dD_2` denotes the region surrounded by `C_1,C_2` and the line `x=adot` If `D_1=D_2,` then the sum of logarithm of possible value of `a` is _____________

Answer

1

Explanation

`"Given that "D_(1)=D_(2)`
`overset(c)underset(1)int((1)/(x)-log x)dx=overset(a)underset(c)int(logx-(1)/(x))dx`
`((-1)/(x^(2))-x(logx-1))_(1)^(c)=(x(logx-1)+(1)/(x^(2)))_(c)^(a)`

`therefore" "0=a(log a-1)+(1)/(a^(2))`
`therefore" "a=1`