#### To determine

**To find:** We have to solve the equation ln(x2-1)=3 for x.

#### Answer

The solution of the equation is x=1+e3.

#### Explanation

**Calculation:** First, we apply the exponential function on both sides of the equation ln(x2-1)=3

Thus, we have

eln(x2-1)=e3,

Since we know that

elnx=x (1)

Thus, using equation (1), we have

x2-1=C

Or x2=e3+1,

x=1+e3

**Conclusion:**

The solution of the equation is x=1+e3.

#### To determine

**To find:** We have to solve the equation e2x-3ex+2=0 for x.

#### Answer

The solution of the equation is either x=0 or x=ln2.

#### Explanation

**Calculation:** First we find the factor of the equation e2x-3ex+2=0

e2x-2ex-ex+2=0,

exex-2-1ex-2=0,

Or, ex-2ex-1=0

So, either ex-2=0 or ex-1=0. If ex-2=0 that is ex=2, then by applying natural

logarithmic on both sides, we have

lnex=ln2 or x=ln2.

If ex-1=0 that is ex=1, then by applying natural logarithmic on both sides, we have

lnex=ln1 or x=0.

Thus, either x=0 or x=ln2.

**Conclusion:**

The solution of the equation is either x=0 or x=ln2.