Find \( x \) in the following equation. \[ \log _{10}(x+5)-\log _{10}(x-5)=1 \] \( x=\square \) (Type a fraction or an integer. Simplify your answer.)

We start with the equation: \[ \log_{10}(x+5) - \log_{10}(x-5) = 1 \] **Step 1.** Use the logarithm property: \[ \log a - \log b = \log\left(\frac{a}{b}\right) \] to combine the logarithms: \[ \log_{10}\left(\frac{x+5}{x-5}\right)= 1. \] **Step 2.** Rewrite the logarithmic equation in exponential form. Recall that if \(\log_{10}(y) = 1\), then: \[ y = 10^1 = 10. \] Thus: \[ \frac{x+5}{x-5} = 10. \] **Step 3.** Solve the equation: \[ x+5 = 10(x-5). \] Expand the right-hand side: \[ x + 5 = 10x - 50. \] **Step 4.** Collect like terms: \[ 5 + 50 = 10x - x, \] which simplifies to: \[ 55 = 9x. \] **Step 5.** Solve for \(x\): \[ x = \frac{55}{9}. \] Thus, the solution is: \[ x=\frac{55}{9}. \]