Question

Josie is trying to find a solution to the equation x = ln(2) +2. She uses her graphing
calculator to graph yı = 2 and y2 = ln(2x) + 2. She gets the following table of
corresponding values.

Between which two integer x- values is there certainly a point of intersection?

A) It cannot be determined from the information given.
B) 3 and 4
C) -1 and o
D) 1 and 2
E) 2 and 3

Answer 1

Considering where these functions cross, we have that the two integer x-values between which there is a certainly a solution are given by:

B) 3 and 4

How do we find where there is a solution?

If in an interval a function starts greater/smaller than another, and this changes, that is, it becomes smaller/greater than the other function, there is a solution in the interval.

In this problem:

• Until x = 3, we have that $y_1 < y_2$.

• From x = 4 onwards, we have that $y_1 > y_2$.

• Considering these two bullet points above, it guarantees that there is a solution between x = 3 and x = 4, hence option B is correct.

You can learn more about logarithmic functions at https://brainly.com/question/25537936