If 3+log _{5} x=2 log _{25} y, then x= | vedclass

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(A) Given the equation: $3+\log _{5} x=2 \log _{25} y$We know that $\log _{25} y = \frac{\log _{5} y}{\log _{5} 25} = \frac{\log _{5} y}{2}$.Substitut

Vedclass · Accepted Answer

$\frac{y}{125}$

Vedclass · Answer

(A) Given the equation: $3+\log _{5} x=2 \log _{25} y$We know that $\log _{25} y = \frac{\log _{5} y}{\log _{5} 25} = \frac{\log _{5} y}{2}$.Substituting this into the equation: $3+\log _{5} x = 2 \cdot \frac{\log _{5} y}{2}$.This simplifies to: $3+\log _{5} x = \log _{5} y$.We can write $3$ as $\log _{5} 125$,so: $\log _{5} 125 + \log _{5} x = \log _{5} y$.Using the property $\log a + \log b = \log(ab)$,we get: $\log _{5}(125x) = \log _{5} y$.By comparing both sides: $125x = y$,which implies $x = \frac{y}{125}$.

If $3+\log _{5} x=2 \log _{25} y,$ then $x=$

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