1983 TYS

Two variables \(x\) and \(t\) are connected by the differential equation \(\frac{\mathrm{d}x}{\mathrm{d}t}=\frac{kx}{10-x}\), where \(0 < x < 10\) where \(k\) is a constant. It is given that \(x=1\) when \(t=0\) and that \(x=2\) when \(t=1\). Find the value of \(t\) when \(x=5\), giving your answer to three significant figures.