If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to
Given that, p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$
p$$^{3}$$=s$$^{6}$$
p =Â s$$^{\frac{6}{3}}$$ = s$$^{2}$$Â Â ...(1)
Similarly, q = s$$^{\frac{6}{4}}$$ = s$$^{\frac{3}{2}}$$  ...(2)
Similarly, r =Â s$$^{\frac{6}{5}}$$Â Â ...(3)
$$\Rightarrow$$ $$log_{s}{(pqr)}$$Â
By substituting value of p, q, and r from equation (1), (2) and (3)Â
$$\Rightarrow$$ $$log_{s}{(s^{2}*s^{\frac{3}{2}}*s^{\frac{6}{5}})}$$Â
$$\Rightarrow$$ $$log_{s}(s^{\frac{47}{10}})$$Â
$$\Rightarrow$$ $$\dfrac{47}{10}$$Â
Hence, option A is the correct answer.Â
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