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We want to solve the following equation. sqrt(2x+8)=5log_(3)(x) One of the solutions is x~~352. Find the other solution. Hint: Use a graphing calculator. Round your answer to the nearest tenth. x~~

We want to solve the following equation.\newline2x+8=5log⁡3(x) \sqrt{2 x+8}=5 \log _{3}(x) \newlineOne of the solutions is x≈352 x \approx 352 .\newlineFind the other solution.\newlineHint: Use a graphing calculator.\newlineRound your answer to the nearest tenth.\newlinex≈ x \approx

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Q. We want to solve the following equation.\newline2x+8=5log⁡3(x) \sqrt{2 x+8}=5 \log _{3}(x) \newlineOne of the solutions is x≈352 x \approx 352 .\newlineFind the other solution.\newlineHint: Use a graphing calculator.\newlineRound your answer to the nearest tenth.\newlinex≈ x \approx
  1. Understand Equation: Understand the equation and the given information.\newlineWe are given the equation 2x+8=5log⁡3(x)\sqrt{2x+8} = 5\log_{3}(x) and we know that one of the solutions is approximately x=352x = 352. We need to find the other solution using a graphing calculator as suggested by the hint.
  2. Set Up for Graphing: Set up the equation for graphing.\newlineTo find the other solution, we can graph the two functions y1=2x+8y_1 = \sqrt{2x+8} and y2=5log⁡3(x)y_2 = 5\log_{3}(x) on a graphing calculator and look for their intersection points.
  3. Graph Functions: Graph the functions on a graphing calculator.\newlineUsing a graphing calculator, input the functions y1=2x+8y_1 = \sqrt{2x+8} and y2=5log⁡3(x)y_2 = 5\log_{3}(x). Make sure to adjust the window settings to include the xx-value of the known solution (x=352x = 352) and to explore a reasonable range around it to find the other solution.
  4. Identify Intersection Points: Identify the intersection points.\newlineAfter graphing, use the calculator's intersection feature to find the points where the two graphs intersect. One of the intersection points will be near x=352x = 352, which is the known solution. The other intersection point will be the other solution we are looking for.
  5. Find Other Intersection Point: Find the xx-value of the other intersection point.\newlineUsing the graphing calculator's intersection feature, locate the xx-value of the other intersection point and round it to the nearest tenth as required.

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