For what value of \( x \) is the following true? \( \log (x+10)=\log x+\log 10 \) Your answer is: \( x=\square \) You may enter the exact value or round to 4 decimal places.

Solve the equation \( \log(x+10)=\log x+\log 10 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\log_{10}{\left(x+10\right)}=\log_{10}{\left(x\right)}+\log_{10}{\left(10\right)}\) - step1: Find the domain: \(\log_{10}{\left(x+10\right)}=\log_{10}{\left(x\right)}+\log_{10}{\left(10\right)},x>0\) - step2: Simplify the expression: \(\log_{10}{\left(x+10\right)}=\log_{10}{\left(x\right)}+1\) - step3: Rewrite in terms of common logarithms: \(\log_{10}{\left(x+10\right)}=\log_{10}{\left(10x\right)}\) - step4: Set the arguments equal: \(x+10=10x\) - step5: Move the variable to the left side: \(x+10-10x=0\) - step6: Subtract the terms: \(-9x+10=0\) - step7: Move the constant to the right side: \(-9x=0-10\) - step8: Remove 0: \(-9x=-10\) - step9: Change the signs: \(9x=10\) - step10: Divide both sides: \(\frac{9x}{9}=\frac{10}{9}\) - step11: Divide the numbers: \(x=\frac{10}{9}\) - step12: Check if the solution is in the defined range: \(x=\frac{10}{9},x>0\) - step13: Find the intersection: \(x=\frac{10}{9}\) The solution to the equation \( \log (x+10)=\log x+\log 10 \) is \( x=\frac{10}{9} \) or \( x=1.\dot{1} \). Rounding to 4 decimal places, the value of \( x \) is approximately 1.1111.