Express as a single logarithm and, if possible, simplify.
\[
\ln x-2[\ln (x-8)+\ln (x+8)]
\]
\[
\ln x-2[\ln (x-8)+\ln (x+8)]=\square
\]
Answer
\(\boxed{\ln\left(\frac{x}{((x - 8)^2*(x + 8)^2)}\right)}\) is the final simplified expression
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 \(\ln\left(\frac{x}{((x - 8) * (x + 8))^2}\right)\)
Step 5 ：\(\boxed{\ln\left(\frac{x}{((x - 8)^2*(x + 8)^2)}\right)}\) is the final simplified expression
