NIMCET 2012 — Mathematics PYQ

Given:

Since $25=5^2$, we can use the property ${\log }_b(a^n)=n{\log }_{b}a$:

Using the base change property ${\log }_{b}a=\frac{1}{{\log }_{a}b}$:

2. Simplify the expression for $x$

Given:

Using the same base change property:

To make it comparable to $y$, let's multiply the numerator and denominator by 2:

Using the property $n{\log }_{b}a={\log }_b(a^n)$:

3. Compare $x$ and $y$

Now we have:

• $x=\frac{2}{{\log }_{5}9}$

• $y=\frac{2}{{\log }_{5}17}$

Since the function $f(t)={\log }_{5}t$ is an increasing function:

When we take the reciprocal (or compare denominators with the same numerator):

Therefore:

Correct Option:

(a) x > y