Solve the logarithmic equation.
log5x + log5(x+2) = log53
Rewrite the left side of the equation as one logarithm, using the properties of logarithms.
log5(x(x+2)) = log53
Next, exponentiate both sides of the equation.
x(x+2) = 3
Now, solve for x. Use the Distributive Property.
x2 + 2x = 3
Set the equation equal to zero.
x2 + 2x -3 = 0
Solve the resulting quadratic equation. Use the Quadratic Formula.
Remember that the domain of logmx is all x > 0, so the answer must be greater than zero.