The value of x is 9.
Given:
The length of the tangent lines are given as, 5x and 7x-18.
The objective is to find the value of x.
The two tangents of a circle drawn from a point outside a circle will always be equal.
Then, the value of x can be solved by,
![\begin{gathered} 5x=7x-18 \\ 5x-7x=-18 \\ -2x=-18 \\ x=-(18)/(-2) \\ x=9 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/x4f3oep1sba35dyvg3nx9jpqe4ea092r1m.png)
Hence, the value of x is 9.