Solve each of the following equations for

Question 1:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 2:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 3:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 4:

Answer:

or

Comparing with , we get

Since

Therefore

Solving we get

Question 5: [2007]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 6: [2013]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 7:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 8:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 9:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 10:

Answer:

Let

Therefore

Comparing with , we get

Since

Therefore

Solving we get

Therefore (imaginary number).

Hence

Question 11:

Answer:

Let

Therefore we have

Comparing with , we get

Since

Therefore

Solving we get

Therefore .

Hence

Question 12:

Answer:

Let

Therefore

Comparing with , we get

Since

Therefore

Solving we get

When

Comparing with , we get

Therefore

Hence

When

Comparing with , we get

Therefore

Hence

Question 13:

Answer:

Let

Therefore

Comparing with , we get

Since

Therefore

Solving we get

When

Comparing with , we get

Therefore

Hence

When

Comparing with , we get

Therefore

Hence

Hence

Question 14:

Answer:

Let

Therefore the equation becomes

or

Comparing with , we get

Therefore

Hence

When y = 2

Squaring both sides

Similarly, when y = 0.5

Hence

Question 15:

Answer:

Let

Therefore

When

When

Hence

Question 16:

Answer:

Let

When

When

Hence

Question 17:

Answer:

Let

When

When

Hence

Question 18: [2006]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 19: [2012]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

If we want only three significant figures than

Question 20: [2014]

Answer:

Comparing with , we get

Since

Therefore

Solving we get

If we want only two significant figures than