Question

How do you solve `ln x - ln (1/x) = 2`?

Answer 1

`x=e`

Explanation:

Since `ln(1/x) = - ln x`, the equation becomes

`2 ln x = 2 implies ln x =1`

So

`x=e`

Answer 2

`x=e`

Explanation:

We have,`(1) log_aX=n<=>X=a^n`
`(2)log_a(M/N)=log_aM-log_aN`
Here,
`lnx-ln(1/x)=2`, Applying (2) ,we get
`=>lnx-[ln1-lnx]=2`
`=>lnx-ln1+lnx=2`, where, `ln1=0`
`=>2lnx=2`
`=>lnx=1=>log_ex=1`, Applying (1) ,we get
`=>x=e^1=e`