So if my ans was helpful u can follow me.
Answer:
e^2 -7 = x
Step-by-step explanation:
2=ln(x+7)
Raise each side to the base of e
e^2 = e^ln (x+7)
The e^ln cancel
e^2 = x+7
Subtract 7 from each side
e^2 -7 = x +7-7
e^2 -7 = x
AB^2 + BC^2 = AC^2
AB^2 + 6^2 = square root 117^2
AB^2 + 36 = 117
Now subtract 117 from both sides
AB^2 = 81
AB = square root 81 = 9

Therefore AB is 9 cms.