x, y and z all are positive number. If 3^x > 9^y and 2^y > 4^z, then which of the following is **TRUE**?

Question 16

$$x, y$$ and $$z$$ all are positive number. If $$3^x > 9^y$$ and $$2^y > 4^z$$, then which of the following is TRUE?

Solution

if we consider : $$3^x > 9^y$$, then x must greater than y and x must greater than 2.

Let say , x=7 and y=3 , it implies that $$3^5=243>9^2=81.$$

again, if we consider : $$2^y > 4^z$$ , then y must greater than z and y must greater than 2.

Let say, z=1, So, y=3 is greater than z.

So, it must be : $$x>y>z.$$

A is correct choice.

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