#### To determine

**To find:** We have to find the solution of 2(1-3x)=99 correct to four decimal places.

#### Answer

The solution of the equation is x≈1.8764.

#### Explanation

**Calculation:**

We have to solve equation 2(1-3x)=99.

**Step 1:** Taking natural logarithmic on both sides of the equation, we get

ln2(1-3x)=ln99 (1)

Since we know that

lnax=xlna (2)

**Step 2:** Now using formula (2) in the equation (1), we have

1-3xln2=ln99

**Step 3:** We solve the equation for x,

1-3x=ln99ln2, or

x=131-ln99ln2

**Step 4:** Now using the scientific calculator, we can calculate the value of x to the four decimal points,

which is x≈1.8764.

**Conclusion:**

The solution of the equation is x≈1.8764.

#### To determine

**To find:** We have to find the solution of lnx+1x=2 correct to four decimal places.

#### Answer

The solution of the equation is x≈0.1565.

#### Explanation

**Calculation:**

We have to solve equation lnx+1x=2.

**Step 1:** Taking the exponential function on both sides of the equation, we get

elnx+1x=e2 (1)

Since we know that

elnx=x (2)

**Step 2:** Now using formula (2) in the equation (1), we have

x+1x=e2

**Step 3:** We solve the equation for x,

1+1x=e2, or

1x=e2-1, or

x=1e2-1.

**Step 4:** Now using the scientific calculator, we can calculate the value of x to the four decimal points,

which is x≈0.1565.

**Conclusion:**

The solution of the equation is x≈0.1565.