help

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

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

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

Now this is the manual calculation which requires some time to solve. If you don't have the concepts and yet want to solve such equations quickly then use online Quadratic Calculator.