CAT 2018 Slot 2 - QUANT Question 28

Question 28

If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to

Solution

Given that, p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$

p$$^{3}$$=s$$^{6}$$

p = s$$^{\frac{6}{3}}$$ = s$$^{2}$$   ...(1)

Similarly, q = s$$^{\frac{6}{4}}$$ = s$$^{\frac{3}{2}}$$   ...(2)

Similarly, r = s$$^{\frac{6}{5}}$$   ...(3)

$$\Rightarrow$$ $$log_{s}{(pqr)}$$ 

By substituting value of p, q, and r from equation (1), (2) and (3) 

$$\Rightarrow$$ $$log_{s}{(s^{2}*s^{\frac{3}{2}}*s^{\frac{6}{5}})}$$ 

$$\Rightarrow$$ $$log_{s}(s^{\frac{47}{10}})$$ 

$$\Rightarrow$$ $$\dfrac{47}{10}$$ 

Hence, option A is the correct answer. 


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