Solve the equation `2log_(3)x+log_(3)(x^(2)-3)=log_(3)0.5+5^(log_(5)(log_(3)8)`

Explanation

This equation can be written as
`log_(3)x^(2)+log_(3)(x^(2)-3)=log_(3)0.5+log_(3)8`
`log_(3)x^(2)+log_(3)(x^(2)-3)=log_(3)(4)`
This is equivalent to the system
`{(x^(2)gt0),(x^(2)-3gt0),(x^(2)(x^(2)-3)=4):}implies{(xlt0 "and" xgt0),(xlt-sqrt(3) "and" xgtsqrt(3)),((x^(2)-4)(x^(2)=1)=0):}`
`impliesx^(2)-4=0:.x=+-2`, but `xgt0`
Consequently `x_(1)=2` is only root of the original equation.