# python3 time-complexity-log.py

import matplotlib.pyplot as plt
import numpy as np
import scipy.special as sp
import math

#plt.rcParams["text.usetex"] = True

x = np.linspace(0.0000001, 10, 1001)

plt.xticks(np.linspace(0, 10, 11))
plt.ylim(0.001, 10000)
plt.yscale('log') 

y = np.log2(x)
plt.plot(x, y, "c", label="$log_2(x)$")

#
# add your codes here for other functions
#

y = sp.factorial(x)
plt.plot(x, y, label="$x!$")

plt.legend(bbox_to_anchor=(0.993, 0.01), loc='lower right', borderaxespad=0, fontsize=10, fancybox=True, framealpha=0.0)
plt.savefig("time-complexity-log.pdf", transparent=True, bbox_inches = 'tight', pad_inches = 0)