Question

plzzz ans.....Thnk you ......Logarithms

Answer 1

Hey there !!!

logxy=log(x/y)+2log2=2

logxy=logx+logy   log(x/y)=logx-logy

So,

logx+logy=logx-logy+2log2=2


logx+logy=2-------Equation 1

logx-logy+2log2=2

logx-logy=2-2log2

logx-logy=2(1-log2)-------Equation 2

Adding equation 1 and 2

   logx+logy=2
+(logx-logy=2(1-log2))
___________________
2logx=2+2(1-log2)

2logx=2(1+1-log2)

logx=2-log2

We know that log10=1

              similarly log100=log10²=2log10=2

So, 2=log100

Now,

logx=2-log2

logx=log100-log2

logx=log(100/2)

logx=log50

⇒⇒x=50

logxy=2

logxy=log100

xy=100

But x=50

So, 50*y=100

  y=100/50=2

So, x=50 y=2

Hope this helped you.................