Solve for \( x \) : \( \log (x+4)-\log (x+3)=2 \) \( x=\square \) You may enter the exact value or round to 4 decimal places.

To solve for \( x \) in the equation \( \log (x+4)-\log (x+3)=2 \), we can use the properties of logarithms. First, apply the logarithmic property that states \( \log a - \log b = \log \left( \frac{a}{b} \right) \): \[ \log \left( \frac{x+4}{x+3} \right) = 2. \] Now, we can convert the logarithmic equation to its exponential form: \[ \frac{x+4}{x+3} = 10^2, \] which simplifies to: \[ \frac{x+4}{x+3} = 100. \] Next, cross-multiply: \[ x + 4 = 100(x + 3). \] Expanding the right side gives: \[ x + 4 = 100x + 300. \] Now, rearranging the equation results in: \[ 4 - 300 = 100x - x, \] which simplifies to: \[ -296 = 99x. \] Dividing by 99 yields: \[ x = -\frac{296}{99} \approx -2.9798. \] Thus, the final answer is: \( x = -\frac{296}{99} \) or approximately \( -2.9798 \).