If logylogx=23 and log(xy)=5, then number of zeros in x×y are

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If { : x}{ : y} = {3}{2} and : (xy) = 5, then number of z

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If $\frac{lo g x}{lo g y} = \frac{3}{2}$ and $lo g (x y) = 5$ , then number of zeros in $x \times y$ are

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\frac{lo g x}{lo g y} = \frac{3}{2}

and

lo g (x y) = 5

, then number of zeros in

x \times y

are

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

\log { xy = 5 } ...(1)\\ \log x + \log y = 5 \mbox{...(Multiplication rule)}\\ \dfrac { \log { x } }{ \log { y } } =\dfrac { 3 }{ 2 } ...(2)\\ \therefore \log x = \dfrac { 3 }{ 2 } \log y\\ So, \dfrac { 3 }{ 2 } \log y + \log y = 5\\ \mbox{Assuming base 10}\\ \dfrac { 5 }{ 2 } \log _{ 10 }{ y } = 5\log _{ 10 }{ 10 } \\ \log { y }^{ \frac { 5 }{ 2 } } = \log { 10 }^{ 5 }\\ \\ So, y = { 10 }^{ 2 }\\ \log x = \dfrac { 3 }{ 2 } \log y \\ \log x = \dfrac { 3 }{ 2 } \log { 10 }^{ 2 } = \log { 10 }^{ 3 }\\ So, x = 1000\\ y = 100\\

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Question Text	If $\frac{lo g x}{lo g y} = \frac{3}{2}$ and $lo g (x y) = 5$ , then number of zeros in $x \times y$ are
Answer Type	Text solution:1
Upvotes	150

If logylogx​=23​ and log(xy)=5, then number of zeros in x×y are

Text solutionVerified

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If $\frac{lo g x}{lo g y} = \frac{3}{2}$ and $lo g (x y) = 5$ , then number of zeros in $x \times y$ are