#### To determine

**To find:** We have to solve the equation 10(1+e-x)-1=3 for x.

#### Answer

The solution of the equation is x=ln37.

**Calculation:**

We have to solve the equation 10(1+e-x)-1=3

We can rewrite this equation as (1+e-x)-1=310 or

(1+e-x)=103, or

**e-x=103-1,** or

(e-x)=73, or

ex=37,

Now taking natural logarithmic on both sides, we have

lnex=ln37, or

x=ln37.

**Conclusion:**

The solution of the equation is x=ln37.

#### Explanation

**Calculation:**

We have to solve the equation 10(1+e-x)-1=3

We can rewrite this equation as (1+e-x)-1=310 or

(1+e-x)=103, or

**e-x=103-1,** or

(e-x)=73, or

ex=37,

Now taking natural logarithmic on both sides, we have

lnex=ln37, or

x=ln37.

**Conclusion:**

The solution of the equation is x=ln37.