2^x*5^y= 1 and 5^(x+1)= 2^(1 – y)
we take log base 10 both sides for both eqns and use properties of logarithms
log(2^x*5^y)= log(1)= 0 or log2^x + log5^y= 0 or xlog2 + ylog5= 0....(1)
and log(5^(x+1))= log(2^(1 – y)) or (x+1)log5= (1 – y)log2......(2)
solving (1) and (2) for x and y, we get
y= log2/(log2+log5)= log2/log(2*5)= log2/log10= log2/1= log2
and x= – log5/(log2+log5)= – log5/log10= – log5/1= log(1/5)
so option C is correct
kindly approve :)