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.)

Answer

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Answer

$\boxed{2x - 10 = 144}$ is the logarithmic equation rewritten without logarithms.

Steps

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.