Question

Помогите пожалуйста.Построить схематически график функции:1)y=log_0.2 x2)y=log_2 x

Answer 1

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Answer 2

Plotting the Functions

To plot the functions y = log_0.2(x) and y = log₂(x), we can start by identifying some key points on the graphs.

For the function y = log_0.2(x): - When x = 1, y = log_0.2(1) = 0, since any number raised to the power of 0 is 1. - When x = 0.2, y = log_0.2(0.2) = 1, since 0.2 raised to the power of 1 is 0.2.

For the function y = log₂(x): - When x = 1, y = log₂(1) = 0, since any number raised to the power of 0 is 1. - When x = 2, y = log₂(2) = 1, since 2 raised to the power of 1 is 2.

Now, let's plot these points on a graph:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0.01, 10, 100)  # Generate 100 x-values from 0.01 to 10

# Plot y = log_0.2(x)
y1 = np.log(0.2) / np.log(x)
plt.plot(x, y1, label='y = log_0.2(x)')

# Plot y = log_2(x)
y2 = np.log2(x)
plt.plot(x, y2, label='y = log_2(x)')

plt.xlabel('x')
plt.ylabel('y')
plt.title('Graphs of y = log_0.2(x) and y = log_2(x)')
plt.legend()
plt.grid(True)
plt.show()

The resulting graph will show the two functions y = log_0.2(x) and y = log₂(x).