#### To determine

**To find:** We have to find the solution of ln1+x3-4=0 correct to four decimal places.

#### Answer

The solution of the equation is x≈3.7703.

#### Explanation

**Calculation:**

We have to solve equation** ln1+x3-4=0** or ln1+x3=4.

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

eln(1+x3)=e4 (1)

Since we know that

elnx=x (2)

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

(1+x3)=e4.

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

x3=e4-1, or

x=(e4-1)1/3.

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

which is x≈3.7703.

**Conclusion:**

The solution of the equation is x≈3.7703.

#### To determine

**To find:** We have to find the solution of 2e1/x=42** ** correct to four decimal places.

#### Answer

The solution of the equation is x≈0.3284.

#### Explanation

**Calculation:**

We have to solve equation 2e1/x=42, or e1/x=21.

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

lne1/x=ln21 (1)

Since we know that

lnex=x (2)

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

1x=ln21

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

x=1ln21.

**Step 4:** Now using the scientific calculator, we can calculate the value of x to the four decimal points, which is x≈0.3284.

**Conclusion:**

The solution of the equation is x≈0.3284.