Question

Solve for x and leave an exact answer

Answer 1

`log_(2) x + log_(2) (x-7) = 3`

`log_(2) (x)(x-7) = 3`

`2^{ log_(2) (x)(x-7)} = 2^(3)`

`x(x-7) = 8`

`x^(2) - 7x -8 = 0`

`\left \{ {{ x_(1) = 8} \atop { x_(2) =-1}} \right.`
Since in
`log_(a) x` x>0, then the answer is x=8 only.
Hope it helps!