Question 1: Simplify each of the following:

(i)

(ii)

(iii)

(iv)

(v)

Question 2: Prove the following

(i)

LHS RHS

(ii)

LHS RHS

(iii)

LHS RHS

(iv)

LHS RHS

(v)

LHS

(vi)

LHS

(vii)

LHS

(viii)

LHS

(ix)

LHS

(x)

LHS

(xi)

LHS

RHS

Hence LHS = RHS

(xii)

LHS

(xiii)

LHS

Question 3: Express each of the following as the logarithm of a single number.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 4: Evaluate the following:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 5: Prove that:

(i)

LHS

RHS . Hence proved.

(ii)

LHS

RHS . Hence proved.

Question 6: If and , express in terms of .

Answer:

Question 7: If and , prove that

Answer:

and

Question 8: If , prove that

Answer:

Question 9: If , prove that

Answer:

Question 10: If , prove that .

Answer:

Question 11: If , prove that

Answer:

Question 12: If , prove that

Answer:

If

Question 13: If , prove that

Answer:

Question 14: If , find the following in terms of

(i)

(ii)

Question 15: If , and , find the value of and

Answer:

Given , and

Therefore

Therefore

Question 16: If and , find the value of and

Answer:

Given and

Therefore

Question 17: If and , express in terms of and .

Answer:

Given

Question 18: If , express in terms of

Answer:

Question 19: If and , express in terms of and .

Answer:

Given and

Question 20: If and , express in terms of and .

Answer:

Given: and

Question 21: Solve the following:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Question 22: If , find and

Answer:

Given

Question 23: If and , find the value of , if

Answer:

Given

Therefore

Question 24: Given and , find the value of each of the following:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 25: Without using tables show that

(i)

LHS

RHS

(ii)