loop and break

loop repeats its block forever, until you leave it with break. It is the right tool when you do not know in advance how many rounds you need.

let mut n = 0;
loop {
    n += 1;
    if n == 3 {
        break;
    }
}

Like if, a loop is an expression. Write a value after break and the whole loop evaluates to it:

let mut tries = 0;
let found = loop {
    tries += 1;
    if tries * tries > 50 {
        break tries; // the loop's value
    }
};
// found == 8

Use continue to skip straight to the next round. Just make sure some path always reaches break, or the program never ends.

Your task

Write first_power_over(base: u64, limit: u64) -> u32. It returns the smallest exponent n (starting at 0) such that base raised to n is strictly greater than limit. Assume base >= 2.

For example first_power_over(2, 100) is 7, because 2^7 = 128 is the first power of two above 100. Build it with a loop that breaks with the answer.