See answer below
You must use the intermediate value theorem
Then there is a value
It is explained below
Or -x = 3 ln x. This expression signifies that for all real x, x cannot be less than or equal to 0.
Now, in the logarithmic equation the LHS has - x, while it has a positive expression 3ln x on the RHS. This would be possible only if x is less than 1
Thus it is proved that x would lie between 0 and 1