Using practical example from the field of mathematics, compare and contrast the relationship between logarithm and indices. Illustrate your understanding of indices and logarithm by discussing and explaining possible three reasons for their relationship.

b) In your own words, clearly distinguish and differentiate between rational numbers and irrational numbers within the context of mathematics. You may use an appropriate number to explain your answer.

c) In your own words, clearly distinguish and differentiate between real numbers and irrational numbers within the context of mathematics. You may use an appropriate number to explain your answer.