Solve the equation \(2 \mathrm { e } ^ { x } = 5\), giving your answer as an exact natural logarithm.
By substituting \(y = \mathrm { e } ^ { x }\), show that the equation \(2 \mathrm { e } ^ { x } + 5 \mathrm { e } ^ { - x } = 7\) can be written as
$$2 y ^ { 2 } - 7 y + 5 = 0$$
Hence solve the equation \(2 \mathrm { e } ^ { x } + 5 \mathrm { e } ^ { - x } = 7\), giving your answers as exact values of \(x\).