If p^3 = q^4 = r^6 = t^7 = s^2,then log_t(pqr | vedclass

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(D) Given:$p^3 = q^4 = r^6 = t^7 = s^2 = k$Express each variable in terms of $k$:$p = k^{1/3}, q = k^{1/4}, r = k^{1/6}, s = k^{1/2}, t = k^{1/7}$Find

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$\frac{35}{4}$

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(D) Given:$p^3 = q^4 = r^6 = t^7 = s^2 = k$Express each variable in terms of $k$:$p = k^{1/3}, q = k^{1/4}, r = k^{1/6}, s = k^{1/2}, t = k^{1/7}$Find the product $pqrs$:$pqrs = k^{1/3} 	imes k^{1/4} 	imes k^{1/6} 	imes k^{1/2} = k^{(1/3 + 1/4 + 1/6 + 1/2)}$Calculate the sum of the exponents:$\frac{1}{3} + \frac{1}{4} + \frac{1}{6} + \frac{1}{2} = \frac{4 + 3 + 2 + 6}{12} = \frac{15}{12} = \frac{5}{4}$So,$pqrs = k^{5/4}$Now evaluate the logarithm:$\log_t(pqrs) = \log_{k^{1/7}}(k^{5/4})$Using the property $\log_{a^n}(b^m) = \frac{m}{n} \log_a(b)$:$\log_{k^{1/7}}(k^{5/4}) = \frac{5/4}{1/7} = \frac{5}{4} 	imes 7 = \frac{35}{4}$

If $p^3 = q^4 = r^6 = t^7 = s^2$,then $\log_t(pqrs) = \ldots$.

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