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.

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


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

(Very confused, any help would be great!)

Answer 1

Explanation:

Part A:

We have two equations in the given question:

y=8x and y=2x+2

Then these two equations will intersect at a point where y is same fro both the equations:

In equation y=8x we will exchange y with the other equation which is y=2x+2 then we would have 8x=2x+2..

Part B:

8x = 2x + 2. Take the integer values of x between −3 and 3

x= -3

8(-3)=2(-3)+2

-24=-6+2

-24= -4

It is false

Now plug x= -2

8(-2)=2(-2)+2

-16 = -4+2

-16 = -2

This is false

Now plug x= -1

8(-1)=2(-1)+2

-8 = -2+2

-8=0

It is false

Now plug x= 0

8(0)=2(0)+2

0=0+2

0=2

It is false

Now plug x= 1

8(1)=2(1)+2

8=2+2

8=4

False

Now plug x= 2

8(2)=2(2)+2

16=4+2

16=6

False

Now plug x=3

8(3)=2(3)+2

24=6+2

24=8

It is false

It means there is no solution to 8x=2x+2 for the integers values of x between −3 and 3

Part C:

Plot the two given functions on a coordinate plane and identifying the point of intersection(values of the variables which satisfy both equations at a particular point) of the two graphs.

The graph is attached. The point of intersection at x =0.333 and value of y = 2.667....