#### To determine

**To find:** We have to solve the inequality lnx<0 for x.

#### Answer

**Answer: x<1.**

#### Explanation

**Calculation:**

We have to solve the inequality lnx<0 .

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

elnx<e0 (1)

Since we know that

elnx=x (2)

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

x<e0,

And since e0=1, so

x<1.

**Conclusion: x<1.**

#### To determine

**To find:** We have to solve the inequality ex>5 for x.

#### Answer

**Answer: x>ln5.**

#### Explanation

**Calculation:** We have to solve the inequality ex>5.

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

lnex>ln5 (1)

Since we know that

lnex=x (2)

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

x>ln5.

**Conclusion: x>ln5.**