Question

if x^2+y^2=8xy then show that 2log (x+y) = log2 +log5 + logX + logY

Answer 1

See the attachment for detail solution.
Hope it will help you

Answer 2

Concept Introduction:

We have to take log on both sides.

Given: $x^2+y^2=8xy$

To Find:

We have to show, $2log (x+y) = log2 +log5 + logX + logY$

Solution:

According to the problem,

$x^2+y^2=8xy$

⇒$x^2+y^2+2xy=8xy+2xy$

⇒$(x+y)^{2} =10xy$

⇒$(x+y)^{2} =2*5*xy$

Taking log on both sides:

$2log (x+y) = log2 +log5 + logX + logY$

Hence proved.

Final Answer:

The value of $2log (x+y) = log2 +log5 + logX + logY$ is proved.

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