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Determine the exact value of the positive constant $k$ such that $\int_{0}^{k} e^{4x}\,dx = \int_{0}^{2k} e^{x}\,dx$.
Mathematics 9709 · AS & A Level · Integration
Determine the exact value of the positive constant $k$ such that $\int_{0}^{k} e^{4x}\,dx = \int_{0}^{2k} e^{x}\,dx$.