If \(6^x - 6^{x-1} = 180\), then the value of \(\dfrac{2x-1}{2x+3}\) is:
\(\dfrac{5}{9}\)
\(6^x-6^{x-1} = 6^{x-1}(6-1) = 5\times6^{x-1} = 180 \Rightarrow 6^{x-1}=36=6^2\).
So \(x-1=2 \Rightarrow x=3\).
\(\dfrac{2x-1}{2x+3} = \dfrac{5}{9}\).
Hence, the value of the expression is \(\tfrac59\).
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