Solve for x 1/2 natural log of x+3- natural log of x=0

$\frac{1}{2} \ln (x + 3) - \ln (x) = 0$

Simplify $\frac{1}{2} \cdot \ln (x + 3) - \ln (x)$ .

Simplify $\frac{1}{2} \ln (x + 3)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln ({(x + 3)}^{\frac{1}{2}}) - \ln (x) = 0$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{{(x + 3)}^{\frac{1}{2}}}{x}) = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.30277563$