Question

Consider the equation log5(x + 5) = x2.

What are the approximate solutions of the equation? Check all that apply.

Answer 1

x ≈ -0.93, x ≈ 1.06

Explanation:

A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)

_____

Comment on the graphical solution

I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.

__

The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).