Determine the approximate solution to the equation 2⋅3^x=10

Question

using a graph.(1 point)
Responses

x≈1.7
x approximately equals 1.7

x≈2
x approximately equals 2

x≈1.5
x approximately equals 1.5

x≈10

Answer 1

To determine the approximate solution to the equation \(2 \cdot 3^x = 10\) using a graph, we can rewrite it in a form that can be visualized on a graph.

We can express it as:

\[ y = 2 \cdot 3^x \]

and plot this function. We are looking for the value of \(x\) where \(y = 10\).

1. Start plotting the function \(y = 2 \cdot 3^x\).
2. Draw a horizontal line at \(y = 10\).
3. The point(s) where the curve intersects the horizontal line represents the solution(s) to the equation \(2 \cdot 3^x = 10\).

You would observe that \(x\) where the graph of \(2 \cdot 3^x\) intersects \(y=10\) is approximately around 1.7.

Thus, based on the provided options, the approximate solution is:

x ≈ 1.7