#### To determine

**To find:** We have to solve the equation e7-4x=6 for x.

#### Answer

The solution of the equation is x=14(7-lnx).

#### Explanation

**Calculation:**

First, we take the natural logarithms of both sides of the equation e7-4x=6. Thus

lne7-4x=ln6,

Since we know that

lnex=x (1)

Thus, using equation (1), we have

(7-4x)=ln6

Or 4x=7-ln6,

x=14(7-lnx)

**Conclusion:**

The solution of the equation is x=14(7-lnx).

#### To determine

**To find:** We have to solve the equation ln3x-10=2 for x.

#### Answer

The solution of the equation is x=13(10+e2).

#### Explanation

**Calculation:**

First, we are applying the exponential function on both sides of the equation

**ln3x-10=2.** Thus

eln(3x-10)=e2

Since we know that

elnx=x (1)

Thus, using equation (1), we have

3x-10=e2

Or 3x=10+e2,

x=13(10+e2).

**Conclusion:**

The solution of the equation is x=13(10+e2).