Bisection Method for Exponential Root

Problem

Implement the bisection method to find the root of $f(x) = e^x - b$ on the interval $[\text{lo}, \text{hi}]$.

The root is $x = \ln(b)$, but you must find it using bisection — not the closed-form formula.

Algorithm: Repeat $n$ times:

1. Compute $\text{mid} = (\text{lo} + \text{hi}) / 2$
2. If $f(\text{mid}) > 0$, set $\text{hi} = \text{mid}$; otherwise set $\text{lo} = \text{mid}$

After $n$ iterations, output $(\text{lo} + \text{hi}) / 2$.

Input Format

Four space-separated values: b lo hi n

Output Format

The midpoint approximation of $\ln(b)$, to 4 decimal places.