Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/csBUekrAfl/

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