<span>The next letter is 'n'. The pattern misses a letter after a pair of letters, for example: 'a' and 'b' are a letter pair, then 'c' is skipped, then the letter pair 'd' and 'e' comes next. For every other letter pair, the order is reversed so they are not in alphabetical order. The next letter pair is 'm' and 'n', and because the pair 'j' and 'k' is in alphabetical order, this pair must be reversed. Therefore, the next letter is 'n'.</span>
An <em>inverse</em> function is any function that "undoes" another function. If we think of the function as some kind of machine that takes in a number as input and produces a number as an output, when we give inverse function the number as in input, we get , our original input, as the output
We need a function that undoes , and the natural choice for undoing an exponent is with a logarithm. Here, our base is , so we'll choose as our inverse function. Let's see how that works:
is the power we have to raise to to get , which is , so