1. If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to
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By: anil on 05 May 2019 02.28 am
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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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.