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Hint:

try to make a table. ex: -2  1

                                       5  2

then try to find the function with y=mx+b.

nice!

Rewrite 72x5⋅y472x5⋅y4 as (6x^2⋅y^2)^2⋅(2x)

Factor 3636 out of 7272.

√36(2)x5⋅y436(2)x5⋅y4

Rewrite 3636 as 6262.

√62⋅2x^5⋅y^4 as 62⋅2x5⋅y4

Factor out x4x4.

√62⋅2(x4x)⋅y462⋅2(x4x)⋅y4

Rewrite x4x4 as (x2)2(x2)2.

√62⋅2((x2)2x)⋅y462⋅2((x2)2x)⋅y4

Rewrite y4y4 as (y2)2(y2)2.

√62⋅2((x2)2x)⋅(y2)262⋅2((x2)2x)⋅(y2)2

Move xx.

√62⋅2((x2)2)⋅(y2)2x62⋅2((x2)2)⋅(y2)2x

Move 22.

√(62((x2)2))⋅(y2)2⋅2x(62((x2)2))⋅(y2)2⋅2x

Rewrite (62((x2)2))⋅(y2)2(62((x2)2))⋅(y2)2 as (6x2⋅y2)2(6x2⋅y2)2.

√(6x2⋅y2)2⋅2x(6x2⋅y2)2⋅2x

Add parentheses.

√(6x2⋅y2)2⋅(2x)(6x2⋅y2)2⋅(2x)

Pull terms out from under the radical.

∣∣6x2⋅y2∣∣√2x|6x2⋅y2|2x

Remove non-negative terms from the absolute value.

6x^2y^2√2x

sorry that it might be unclear, but the answer is above.

log₁₀ 10000 = y

From the definition of logs:

Log₁₀  x = y         exactly if 10^y    =   x

log₁₀ 10000 = y        if    10^y =10000         for 10^y=10000    ,    y MUST = 4

\(f(x)=\frac{x^2-1}{1-x}\)

\(g(x)=x+2\)

find and simplify:

f(g(2))-g(f(2)) 

well, let's start with 
f(g(2)) it is composite so the inside then the outside i.e let's start with g(2)

we know that:

g(x)=x+2

so, g(2)=2+2=4 

subsituite g(2) by 4 in f(g(2))

f(4) 

well we know that 
\(f(x)=\frac{x^2-1}{1-x}\)

\(f(4)=\frac{4^2-1}{1-4}=\frac{15}{-3}=-5\)

So we know that f(g(2))= -5 

Now let's do the same for g(f(2))

\(f(2)=\frac{3}{-1}=-3\)

\(g(-3)=-3+2=-1\)

so, g(f(2)) = -1

f(g(2))-g(f(2))= -5-(-1) = -5+1=-4 

It is not so difficult to solve this kind of questions. You just have to follow basic steps

1) Solve for x over the real numbers:
2^(2 x) + 2^(2 x + 1) = 3/8

2) Simplify and substitute y = 2^(2 x).
2^(2 x) + 2^(2 x + 1) = 3×2^(2 x) = 3 y:
3 y = 3/8

3) Divide both sides by 3:
y = 1/8

4) Substitute back for y = 2^(2 x):
2^(2 x) = 1/8

5) Take the logarithm base 2 of both sides:
2 x = -3

6) Divide both sides by 2:
x = -3/2

Another method:

2^(2x+1) =2^2x *2¹

Sub in to the original equation

2^2x * 2   +  2^2x  = 3/8

2^2x * 3 = 3/8

2^2x = 1/8       take log of both sides

2x log 2 = log 1/8

x =  1/2 *  log (1/8) / log2   = -1.5

Let xy=k, so that y = k/x.

Substitute this into the first equation to get  \(x^2 - 20x^2 - 7k = 0\)

Solve this (using the usual formula) as a quadratic in x squared to get

\(x^2 = 10 \pm \sqrt{100 + 7k}\)

The original equations are symmetric in x and y so repeating the procedure will produce an identical result for y.

Since x and y are different, one will have the positive sign in the middle, the other the negative sign.

Multiplying the two results produces (difference between two squares)

\(x^2 y^2 = 100 - (100 + 7k) = -7xy\)

Since xy is not equal to 0,  it follows that xy = -7.

We know angle of incidence = angle of reflection, but we'll ned the diagram of the room to find the third wall strike point !  

Solve for x over the real numbers:
2^(2 x) + 2^(2 x + 1) = 3/8

Simplify and substitute y = 2^(2 x).
2^(2 x) + 2^(2 x + 1) = 3×2^(2 x)
 = 3 y:
3 y = 3/8

Divide both sides by 3:
y = 1/8

Substitute back for y = 2^(2 x):
2^(2 x) = 1/8

Take the logarithm base 2 of both sides:
2 x = -3

Divide both sides by 2:

x = -3/2

I used a graphical approach (desmos) to graph the two equations you will see the following sets of coordinates satisfy the equations :

x,y  = (-1.7 , 4.1)     (-4.1, 1.7)   and   (4.1, -1.7)  and (1.7, - 4.1)

0,0    -3.6, 3.6   and  3.6, -3.6     5.2 , 5.2     -5.2, -5.2 also work, but the absolute values of x and y are equal at these points, so they do not satisfy the question.

Here is the graph:

Solve for x:
2 x + 0.353 = x^2 + 6/17

2 x + 0.353 = 2 x + 353/1000:
2 x + 353/1000 = x^2 + 6/17

Subtract x^2 + 6/17 from both sides:
-x^2 + 2 x + 1/17000 = 0

Multiply both sides by -1:
x^2 - 2 x - 1/17000 = 0

Add 1/17000 to both sides:
x^2 - 2 x = 1/17000

Add 1 to both sides:
x^2 - 2 x + 1 = 17001/17000

Write the left hand side as a square:
(x - 1)^2 = 17001/17000

Take the square root of both sides:
x - 1 = (3 sqrt(1889/170))/10 or x - 1 = -(3 sqrt(1889/170))/10

Add 1 to both sides:
x = 1 + (3 sqrt(1889/170))/10 or x - 1 = -(3 sqrt(1889/170))/10

Add 1 to both sides:

x = 1 + (3 sqrt(1889/170))/10    or      x = 1 - (3 sqrt(1889/170))/10

x = 2                                                               x =x≈-0.000029411