**Evaluate the following limits:**

**Question 1. **

**Solution:**

We have,

=

=

=

=

=

=

We know,. So, we have,

= 4 log 5

**Question 2. **

**Solution:**

We have,

=

=

We know,. So, we have,

=

As, we get,

=

**Question 3. **

**Solution:**

We have,

=

=

=

As, we get,

=

= (log

_{e}a)^{2}

**Question 4. ****, n≠0**

**Solution:**

We have,

=

=

As, we get,

=

=

**Question 5. **

**Solution:**

We have,

=

=

=

=

As, we get,

= log a + log b

= log (ab)

**Question 6. **

**Solution:**

We have,

=

=

=

=

=

=

As, we get,

= (log 3 − log 2)

^{2}=

**Question 7. **

**Solution:**

We have,

=

=

=

=

As, we get,

= 2(log2)

^{2}

**Question 8. **

**Solution:**

We have,

=

=

=

=

As, we get,

= m log a − n log b

= log a

^{m}− log b^{n}=

**Question 9. **

**Solution:**

We have,

=

=

=

As, we get,

= log a + log b + log c

= log (abc)

**Question 10. **

**Solution:**

We have,

=

Let x − 2 = h. So, we get,

=

=

=

=

We know,. So, we have,

= log a

**Question 11. **

**Solution:**

We have,

=

=

=

As, we get,

= log 5 + log 3 + log 2

= log (5×3×2)

= log 30

**Question 12. **

**Solution:**

We have,

=

Let 1/x = h. We get,

=

=

As, we get,

= log a

**Question 13. **

**Solution:**

We have,

=

=

=

=

=

=

Asand, we get,

=

=

=

**Question 14. **

**Solution:**

We have,

=

=

=

As, we get,

= log a + log b − log c − log d

= log a+ log b − (log c + log d)

= log ab − log cd

=

**Question 15. **

**Solution:**

We have,

=

=

Asand, we get,

= log e + 1

= 1 + 1

= 2