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 $x$ .
(Do not simplify. Use integers or fractions for any numbers in the equation.)

Answer

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Answer

$2 x - 10 = 144$ 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 $2 x - 10 = 144$ .

Step 5 ： $2 x - 10 = 144$ is the logarithmic equation rewritten without logarithms.