Using the properties of logarithms, we can simplify the left-hand side of the equation as follows:
Log 10 (x) + Log 10 (y) = Log 10 [(x)(y)]
Then, we can rewrite the right-hand side of the equation using the power rule of logarithms:
2 Log 10 (x+1) = Log 10 [(x+1)^2]
Substituting these expressions back into the original equation, we get:
Log 10 [(x)(y)] = Log 10 [(x+1)^2]
Using the fact that Log 10 (a) = Log 10 (b) if and only if a = b, we can drop the logarithm on both sides of the equation:
(x)(y) = (x+1)^2
Expanding the right-hand side, we obtain:
(x)(y) = x^2 + 2x + 1
Solving for y, we get:
y = (x^2 + 2x + 1)/x
Therefore, y can be expressed in terms of x as:
y = x + 2 + 1/x