Express as a single logarithm and, if possible, simplify.
$\ln x - 2 [\ln (x - 8) + \ln (x + 8)]$
$\ln x - 2 [\ln (x - 8) + \ln (x + 8)] = ◻$

Answer

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Answer

$\ln (\frac{x}{((x - 8)^{2} * (x + 8)^{2})})$ is the final simplified expression

Steps

Step 1 ：Given the expression $\ln x - 2 [\ln (x - 8) + \ln (x + 8)]$

Step 2 ：Combine the two logarithms inside the brackets to get $\ln x - 2 \ln ((x - 8) * (x + 8))$

Step 3 ：Move the 2 in front of the brackets to the exponent of the expression inside the brackets to get $\ln x - \ln ((x - 8) * (x + 8))^{2}$

Step 4 ：Combine the two resulting logarithms into a single logarithm to get $\ln (\frac{x}{((x - 8) * (x + 8))^{2}})$

Step 5 ： $\ln (\frac{x}{((x - 8)^{2} * (x + 8)^{2})})$ is the final simplified expression