Determine the approximate solution to the equation 2⋅3x=10 using a graph.(1 point) Responses x≈2 x approximately equals 2 x≈10 x approximately equals 10 x≈1.7 x approximately equals 1.7 x≈1.5

Answer 1

To solve the equation \(2 \cdot 3^x = 10\) graphically, we can rewrite it as two functions:

1. \(y_1 = 2 \cdot 3^x\)
2. \(y_2 = 10\)

Now, we plot these two functions on a graph.

1. The function \(y_1 = 2 \cdot 3^x\) is an exponential function that grows rapidly as \(x\) increases.
2. The line \(y_2 = 10\) is a horizontal line.

To find the approximate solution, we look for the point where the two graphs intersect.

After plotting the graphs or estimating, we can see that the intersection occurs around \(x \approx 1.7\).

Thus, the approximate solution to the equation \(2 \cdot 3^x = 10\) is:

x ≈ 1.7