Solve the following logarithmic equation. Express irrational solutions in exact fo \[ 2 \log _{12}(x-7)+\log _{12} 4=2 \] Rewrite the given equation without logarithms. Do not solve for $\mathrm{x}$. (Do not simplify. Use integers or fractions for any numbers in the equation.)

Step 1 ：Given the logarithmic equation \(2 \log _{12}(x-7)+\log _{12} 4=2\).

Step 2 ：We can use the property of logarithms that states \(\log_b a = c\) is equivalent to \(b^c = a\).

Step 3 ：Applying this property to each term in the equation to convert it into an exponential form.

Step 4 ：The equation in exponential form is \(2x - 10 = 144\).

Step 5 ：\(\boxed{2x - 10 = 144}\) is the logarithmic equation rewritten without logarithms.