在python中求解指数方程

Question

This code solves for the exponent in x^n + y^n - z^n = 0 by brute force. Would there be a faster and cleaner way to do this?

import math
for n in range(-10, 100000000):
    n /= 1000000.0   
    x =  16**(n)+20**(n)-25**(n)  #formula to solve must equal zero
    if round(x,2) == 0:
        print('exponent is: ',n, ', error is: ',x); break

Answer 1

You can define your function that should be minimized (in your case equal to zero):

def f(n):
    return 16**(n) + 20**(n) - 25**(n)

and then import minimize_scalar from scipy.optimize and solve your equation for n .

from scipy.optimize import minimize_scalar

minimize_scalar(f)

-------------------------------
fun: 0.0
nfev: 55
nit: 35
success: True
x: -518.3839114719358 # x is your n that solves your equation
-------------------------------

Check:

f(-518.3839114719358) # -> 0.0

Checkout the documentation for more. There are additional options you can give the function (like bounds). You also can access each output value (like x , niter , and so on). Besides, the computation really is a no-timer.