Write as a single logarithm. Assume that variables represent positive numbers. \[ 11 \log _{10} x+12 \log _{10} z \]

Step 1 ：Rewrite the expression using the property \(n \log _{a} b = \log _{a} b^n\), so the expression becomes \(\log _{10} x^{11} + \log _{10} z^{12}\)

Step 2 ：Combine the two logarithms into one using the property \(\log _{a} b + \log _{a} c = \log _{a} (b \cdot c)\), so the expression becomes \(\log _{10} (x^{11} \cdot z^{12})\)

Step 3 ：So, the expression \(11 \log _{10} x+12 \log _{10} z\) can be written as a single logarithm as \(\boxed{\log _{10} (x^{11} \cdot z^{12})}\)