The a is Right Where it Should Be

Calculus Level 3

\[\displaystyle \sum_{x=1}^{\infty} \left [ \ln\left(\dfrac{x+4}{x}\right)-\ln\left(\dfrac{x+6}{x+2}\right) \right ] =\ln(a)\]

Evaluate the following sum above and solve for the value of \(a\).

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