log(x+y)=log x +log y, then x=

To solve for x, follow these algebraic steps:

Apply logarithmic properties: Use the product rule for logarithms, which states that log(a) + log(b) = log(ab).

The equation log(x+y) = log x + log y becomes:
log(x + y) = log(xy)

Equate the arguments: Since the logs on both sides have the same base, you can set the arguments equal to each other:

x + y = xy

Rearrange the terms to isolate x: Move all terms containing x to one side of the equation.

y = xy - x

Factor out x:

y = x(y - 1)

Solve for x: Divide both sides by (y - 1):

x = y / (y - 1)