{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e71fcbbb",
   "metadata": {},
   "source": [
    "# [Largest Exponential](https://projecteuler.net/problem=99)\n",
    "\n",
    "Instead of trying to compare the powers $x^y$ directly, compare their logarithms $y\\log{x}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0180569c",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"txt/0099_base_exp.txt\") as f:\n",
    "    pairs = tuple(tuple(int(x) for x in line.split(\",\")) for line in f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a0c22c9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(709, (895447, 504922))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logpows = {(x, y): y * log(x) for (x, y) in pairs}\n",
    "max(enumerate(logpows, start=1), key=lambda x: logpows[x[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a4a2222",
   "metadata": {},
   "source": [
    "#### Copyright (C) 2025 filifa\n",
    "\n",
    "This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
   ]
  }
 ],
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   "codemirror_mode": {
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