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Determine the approximate solution to the equation \( 2 \cdot 3^{x}=10 \) using a graph. (1 point) \( x \approx 1.7 \) \( x \approx 10 \) \( x \approx 1.5 \) \( x \approx 2 \)

Ask by Warner Jimenez. in the United States
Mar 14,2025

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The approximate solution is \( x \approx 1.5 \).

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To approximate the solution to the equation \( 2 \cdot 3^{x}=10 \) using a graph, you would first plot the two functions: \( y = 2 \cdot 3^{x} \) and \( y = 10 \). The point where these two curves intersect gives you the value of \( x \). By looking closely at the intersection point, you'd find that it occurs around \( x \approx 1.7 \). This graphical method helps visualize how exponential growth behaves compared to a constant value. It shows that as \( x \) increases, \( 2 \cdot 3^{x} \) rises rapidly, indicating how exponential functions can outpace linear growth, giving you hints on where to look for solutions!

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