Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^x + 2 intersect are the solutions of the equation 8^x = 2^x + 2. (4 points)

Part B: Make tables to find the solution to 8^x = 2^x + 2. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 8^x = 2^x + 2 graphically? (2 points)

Answer 1

Answer + Step-by-step explanation:

Part A :

Let M(a , b) be a point where the graphs

of the equations y = 8ˣ and y = 2ˣ⁺² intersect.

M lies on both graphs

Then

the coordinates of M verify both equations (equation of graph1 and equation of graph 2)

Then

`b=8^(a)\ \text{on the other hand} \ b=2^(a+2)`

Then

`8^(a)=2^(a+2)`

Therefore ‘a’ (the x-coordinates of the points M where the two graphs intersect) is a solution to the equation :

`8^(x)=2^(x+2)`

Part B : check the attached table.

Part C :

Graphically, we try to spot the points of intersection of the two graphs ,the x-coordinates of those points are the solution to our equation.

In our case , obviously the two graphs intersect at only one point M(1 ,8)

Therefore 1 is the only solution to 8ˣ = 2ˣ⁺².

Also ,Check the attached graph.