Question 15

Explanation

We will simplify the forms of P and Q first.

Simplifying P

Recall that $a^2 - b^2 = (a - b)(a + b)$. Note that $16^x = (4^x)^2$.

Simplifying Q

Similarly, note that $16^{-x} = (4^{-x})^2$.

Analyzing the Value of P

Given $1 < x < 2$.

Analyzing the Value of Q

Given $1 < x < 2$. Multiply by $-1$ (inequality signs flip).

Comparing P and Q

From the results above, we get:

• $P > 5$
• $Q < \frac{5}{4} = 1.25$

It is clearly visible that the value of $P$ is always greater than $Q$ for the given range of $x$.

So, $P > Q$.