Solving 2^x + 2/2^x = 3

[late6002]

2^x + 2/2^x =3

 

[kaliprasad]

In future kindly inform what you have tried and where you are stuck so that we can provide steps to proceed

For this put $2^x = y$ and see what you get

 

[anemone]

Hi late6002, welcome to MHB!

For your information, the cited equation can be reduced to quadratic equation...

 

[HOI]

Since this has been here over a month now (and I just can't resist answering):

The equation is 2^x+ 2/2^x= 3. Following Kaliprasad's advice, let y= 2^x. Then the equation becomes, y+ 2/y= 3. Multiply both sides by y to get y^2+ 2= 3y. As anemone said, that is a quadratic equation, y^2- 3y+ 2= 0. And that is easy to factor: (y- 2)(y- 1)= 0. Either y= 2 or y= 1. Since y= 2^x, if y= 2, 2= 2^x so x= 1. If y= 1, 1= 2^x so x= 0.

Check: if x= 0, 2^x= 2^0= 1 so 2^x+ 2/2^x= 1+ 2/1= 1+ 2= 3. If x= 1, 2^x= 2^1= 2 so 2^x+ 2/2^x= 2+ 2/2= 2+ 1= 3.