Numerical solution of equations — practice question

With $\int_1^a \frac{\ln x}{x^2}\,dx = \frac{2}{5}$, show that $a = \frac{5}{3}(1 + \ln a)$.

Use an iteration formula derived from $a = \frac{5}{3}(1 + \ln a)$ to determine $a$ correct to 2 decimal places. Start from $4$ and give each iterate to 4 decimal places.