Question

Is anyone able to help me with this question, if you understand it ?

Answer 1

Answer:

x ≈ 1.24372255 , 3.87970168

Answer 2

x ≈ 1.2437, 3.8797 (two solutions)

Explanation:

You want the solution(s) to the equation (2^x)/5 = 5·log(x) by finding the points of intersection using a graphing calculator.

Graph

The first attachment shows the graph on a TI-84 work-alike calculator, along with the points of intersection to 5 significant figures.

The solutions are ...

• x ≈ 1.2437
• x ≈ 3.8797

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Additional comment

When the graphing calculator can give you function values even as you type the function arguments, you can find the solutions to full calculator precision as quickly as you can type them. Many graphing calculators now offer the capability to compute a derivative, so writing the Newton's method iterator for the solution is easy to do.

In the second attachment, this is shown as the function f₁(x). Its value is equal to its argument where f(x) = 0. We have defined f(x) as the difference between the two sides of the equation. The graph can give a starting point for the iteration. The full-precision solutions to the equation are ...

x ≈ 1.24372255689, 3.87970168202

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