#### To determine

**To find:** We have to solve the equation 2x-5=3 for x.

#### Answer

The solution of the equation is x=5+ln3ln2.

#### Explanation

**Calculation:** First, we are taking natural logarithmic on both sides of the equation 2x-5=3

. Thus, we have

ln2x-5=ln3

Since we know that

lnax=xlna (1)

Thus, using equation (1), we have

(x-5)ln2=ln3,

Or x-5=ln3ln2

x=5+ln3ln2.

**Conclusion:**

The solution of the equation is x=5+ln3ln2.

#### To determine

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

#### Answer

The solution of the equation is x=1±1+4e2.

#### Explanation

Formula used: lna+lnb=lnab and elnx=x

Calculation: lnx+lnx-1=1,

Using the above formula, we have

ln(xx-1)=1.

Now, by applying exponential function on both sides, we have

eln(xx-1)=e1,

and using above formula we have,

x(x-1)=e, or

x2-x-e=0, or

x=1±1+4e2.

**Conclusion:** The solution of the equation is x=1±1+4e2.