Final answer:
The solution to the equation ((1/3)^(x-2)=50 lies between -6 and -5.
Step-by-step explanation:
To find the integers between which the solution to ((1)/(3))^(x-2)=50 lies, we need to solve the equation for x. Taking the logarithm of both sides, we get x - 2 = log₃(50). Converting log₃(50) to a decimal, we find that x - 2 ≈ 3.874. So the solution to the equation lies between x = 3.874 and x = 3.874 + 2 = 5.874. Since we are looking for integers, the solution lies between -6 and -5.