#### To determine

**To find:** We have to solve equation ** ln2x+1=2-lnx** for x.

#### Answer

The solution of the equation is x=-1±1+8e24.

#### Explanation

**Calculation:**

We have to solve equation** ln2x+1=2-lnx**

**Step 1:** First we rearrange the equation by taking the term -lnx on left side of the equation.

ln2x+1+lnx=2, or

ln(x2x+1)=2 (1)

**Step 2:** Now applying the exponential function on both sides of the equation (1), we have

eln(x2x+1)=e2, or

x2x+1=e2, or

2x2+x-e2=0,

Now, the root of this quadratic equation is given as

x=-1±1+8e24.

**Conclusion:**

The solution of the equation is x=-1±1+8e24