Question

X 2+y2=25xy then prove that 2log (x+y)=3+logx+logy​

Answer 1

                      Answer

We have,

           x^2+y^2=25 (x y) .......(1)

we have to prove,

      2 log(x+y)  = 3+log(x)+log(y)

Step-by-step explanation:

hence,

       >>RHS

        >> (x+y)^2        {:-  a log b = b^a }

                                                     

       

      >> x^2 + y^2 + 2xy

putting value of (1) in equation we get,

 <>  25xy + 2xy = 27 xy

  <> (3^3) *(xy)

Taking log we get,

 <> log 3^3 + log xy      

<> 3 + log xy                          {b^y = x  ,  logb (x)= y}

Hence ,

     RHS = LHS

HENCE PROVED.

I HOPE IT HELPS.

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