Part A- Explain why the xcoordinates of the points where the graphs of the equations y=4^x and y=2^x^+^2 intersect are the solutions of the equation 4^x = 2^x^+^2?

Question

Part A- Explain why the xcoordinates of the points where the graphs of the equations y=4^x and  y=2^x^+^2 intersect are the solutions of the equation 4^x = 2^x^+^2?

anonymous · Answer

@undeadknight26

anonymous · Answer

marry me? yes no? :DDD

anonymous · Answer

uhm nothing special here..... and can you help with this problem?

campbell_st · Answer

The point of intersection is a common point, which is part of both curves. The x value is common to both and produces the commo y value from the point when substituted into both equations.

anonymous · Answer

so just find the point of intersection? @campbell_st

anonymous · Answer

uhmmm

campbell_st · Answer

well it can be solved aglebraically 

but you need the same base... 

$$4^x = (2^2)^x = 2^{2x}$$

so it looks like you equation can be written as 

$$2^{2x} = 2^{x + 2}$$

is this is the case then you just equate the powers and solve

2x = x + 2

campbell_st · Answer

another solution that can be used is to just use a graphing package or site like https://www.desmos.com/calculator

anonymous · Answer

so wait the point f intersection would be 2x?

campbell_st · Answer

no if I had your equation correct

the x value of the point of intersection is the solution to 

2x = x + 2

campbell_st · Answer

if you solve this x = 2

so to check does 

$$4^2 = 2^{2 + 2}~~?$$

anonymous · Answer

oh ok thank you so could you help me with part b and c too?

campbell_st · Answer

so what is part b and c

campbell_st · Answer

can I check the equation is 

$$4^x = 2^{~x + 2}$$

anonymous · Answer

oh oops lol sorry here Part B- Make tables to find the solution to 4^x = 2^x^+^2. Take the integer values of x between -3 and 3.

anonymous · Answer

and yes

campbell_st · Answer

ok... so table of values  so substitute the x values into each equation

x               |  -3    |  -2    |  -1    | 0  | 1  | 2  | 3  |
--------------------------------------------
4^x           | 1/64 | 1/16 |  1/4  | 0 |   4 | 16 | 64|
--------------------------------------------
2^(x + 2) | 1/2   |   1     |    2    | 4  |  8 | 16  | 32


and you see when x = 2 4^x = 16   and 2^(x + 2= 16

anonymous · Answer

ok you los me I know how to substitute them but there are 2 number?.....

campbell_st · Answer

well rather than do 2 tables I used 1 set of x values 

and have 2 rows for the different y values 

1st row is 
$$y = 4^x$$

2nd row is 

$$y = 2^{~x + 2}$$

campbell_st · Answer

so reading the table, the point of intersection is (2, 16)

anonymous · Answer

uhm sorry today just isn't my day im having a total brain fart right not 
ok ok im kinda following

campbell_st · Answer

I can't help with C as I'm in Australia and need to go to class.

campbell_st · Answer

hope it all makes some sense