Jasmyn is standing at the point of tangency to a wishing
well, 27 feet from a bench. Her friend Willard is at the other
point of tangency. Determine the value of x.
w
(2x - 7) ft
27 ft
Sac

The value of   .

Step-by-step explanation:

Diagram of the given scenario shown below.

Given that,

Distance from bench to Jasmyn is   .

Distance from bench to Willard is .

From the Question,

The given wishing well is a circle and all the distance are tangent to the circle.

So, Triangle formed by these points are such as Δ and Δ.

Now, taking both Δ and Δ.

   ⇒                                                 {Radius of circle are equal}

   ⇒                                                 {Common side}

   ⇒          ∠ ∠                              {radius is always perpendicular                                                                          

                                                                           to the point of tangent }

∴            Δ ≅ Δ                                  {By SAS congruence theorem}

Therefore,           ....(1)                             {corresponding part of

                                                                           congruence triangle (CPCT)}

Thus,

   ⇒                                                 {from equation (1)}

   ⇒                          

   ⇒                        

Hence, The value of   .

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)