If \(6^x - 6^{x-1} = 30\), then the value of \(\dfrac{2x-1}{2x+3}\) is:
\(\tfrac{3}{7}\)
\(6^x - 6^{x-1} = 30\) can be written as \(6^{x-1}(6-1) = 30\), so \(6^{x-1}\times5=30\).
This gives \(6^{x-1}=6\), so \(x-1=1\), meaning \(x=2\).
Substituting into the required expression: \(\dfrac{2x-1}{2x+3} = \dfrac{2(2)-1}{2(2)+3} = \dfrac{3}{7}\).
Hence, the value of the expression is \(\tfrac{3}{7}\).
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