Largest exponential : Problem 99 : Project Euler

Largest exponential : Problem 99 : Project Euler

Comparing two numbers written in index form like 2¹¹ and 3⁷ is not difficult, as any calculator would confirm that 2¹¹ = 2048 < 3⁷ = 2187.
However, confirming that 632382⁵¹⁸⁰⁶¹ > 519432⁵²⁵⁸⁰⁶ would be much more difficult, as both numbers contain over three million digits.
Using base_exp.txt (right click and 'Save Link/Target As...'), a 22K text file containing one thousand lines with a base/exponent pair on each line, determine which line number has the greatest numerical value.

NOTE: The first two lines in the file represent the numbers in the example given above.

This is on of the easiest problem of Project Euler! Instead of calculating a^x and b^y actually to determine which one is greater, use the fact from analysis that log x is an increasing function. therefore if  a^x > b^y => x*log a > y*log b

Python Code

import math

def largestExponential():

    maxBE = 0.0

    maxLineNumber = 0

    lineNumber = 1

    val = 0.0

    f = open('base_exp.txt','r')

    for line in f:

        t = line[0:len(line)-1]

        mylist = t.split(",")

        val = float(mylist[1])*math.log(float(mylist[0]))

        if maxBE <= val:

            maxBE = val

            maxLineNumber = lineNumber

        lineNumber = lineNumber + 1   

    print("Maximum value at line Number",maxLineNumber)

largestExponential()