Exponential curve and its reflected logarithmic curve

The curve \(C_1\) has equation \(y=a(b^x)+c\), where \(a\), \(b\) and \(c\) are constants and \(b>0\). \(C_1\) passes through \((0,5)\) and \((1,7)\), and has the line \(y=3\) as an asymptote.

1. Find \(a\), \(b\) and \(c\).[3]
2. The curve \(C_2\), with equation \(y=\log_2(x-h)+k\), is the reflection of \(C_1\) in the line \(y=x\). Find \(h\) and \(k\).[3]
3. State the equation of the asymptote of \(C_2\) and the coordinates of the point where \(C_2\) meets the \(x\)-axis.[2]