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.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q