25 points
approximate the solution to the equation above using three iterations of successive approximation. use the graph below as a starting point.

Step-by-step explanation:

We can use Newton's method to solve this kind of problems.

It is a method of computing fixed points of iterated functions, the equation is given by:

So, first of all we need to identify the function.

We know that our equation is:

Let's simplify and rewrite this equation using the natural log.

and if we put all these terms on the left side we will get the function.

f'(x) is the first derivative of the function, Let's take the derivative.

Now, using the graph we choose x₁ = 0.6 as a starting point. Let's recall we need to find the intersection point, so we must choose a value of x as close as possible to the intersect point.

We need to put x₂ in the equation again and find x₃

Therefore the approximate solution is 0.85.

I hope it helps you!

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