Answer :
To graph the logarithmic function \( g(x) = 4 \log_2(x) \), we need to plot some points on the graph of the function. Let's find the y-values for two specific x-values and then plot these points.
### Step-by-Step Solution:
1. Identify the function:
The function given is \( g(x) = 4 \log_2(x) \).
2. Choose x-values and find corresponding y-values:
- Point 1:
- Let's take \( x_1 = 1 \).
- To find \( y_1 \), we plug \( x_1 \) into the function \( g(x) \):
[tex]\[ y_1 = 4 \log_2(1) \][/tex]
- The logarithm base 2 of 1 is:
[tex]\[ \log_2(1) = 0 \][/tex]
- So,
[tex]\[ y_1 = 4 \cdot 0 = 0 \][/tex]
- Therefore, the first point is:
[tex]\[ (x_1, y_1) = (1, 0) \][/tex]
- Point 2:
- Let's take \( x_2 = 2 \).
- To find \( y_2 \), we plug \( x_2 \) into the function \( g(x) \):
[tex]\[ y_2 = 4 \log_2(2) \][/tex]
- The logarithm base 2 of 2 is:
[tex]\[ \log_2(2) = 1 \][/tex]
- So,
[tex]\[ y_2 = 4 \cdot 1 = 4 \][/tex]
- Therefore, the second point is:
[tex]\[ (x_2, y_2) = (2, 4) \][/tex]
### Plotting the Points:
- The first point on the graph is \( (1, 0) \).
- The second point on the graph is \( (2, 4) \).
These points should be plotted on the Cartesian plane. Once plotted, they will help us visualize the graph of the function \( g(x) = 4 \log_2(x) \). The graph will pass through these points and follow the typical shape of a logarithmic function, which increases slowly and stretches vertically due to the factor of 4.
By properly plotting these points, you will get a clear visualization of how the function behaves for different values of [tex]\( x \)[/tex].
### Step-by-Step Solution:
1. Identify the function:
The function given is \( g(x) = 4 \log_2(x) \).
2. Choose x-values and find corresponding y-values:
- Point 1:
- Let's take \( x_1 = 1 \).
- To find \( y_1 \), we plug \( x_1 \) into the function \( g(x) \):
[tex]\[ y_1 = 4 \log_2(1) \][/tex]
- The logarithm base 2 of 1 is:
[tex]\[ \log_2(1) = 0 \][/tex]
- So,
[tex]\[ y_1 = 4 \cdot 0 = 0 \][/tex]
- Therefore, the first point is:
[tex]\[ (x_1, y_1) = (1, 0) \][/tex]
- Point 2:
- Let's take \( x_2 = 2 \).
- To find \( y_2 \), we plug \( x_2 \) into the function \( g(x) \):
[tex]\[ y_2 = 4 \log_2(2) \][/tex]
- The logarithm base 2 of 2 is:
[tex]\[ \log_2(2) = 1 \][/tex]
- So,
[tex]\[ y_2 = 4 \cdot 1 = 4 \][/tex]
- Therefore, the second point is:
[tex]\[ (x_2, y_2) = (2, 4) \][/tex]
### Plotting the Points:
- The first point on the graph is \( (1, 0) \).
- The second point on the graph is \( (2, 4) \).
These points should be plotted on the Cartesian plane. Once plotted, they will help us visualize the graph of the function \( g(x) = 4 \log_2(x) \). The graph will pass through these points and follow the typical shape of a logarithmic function, which increases slowly and stretches vertically due to the factor of 4.
By properly plotting these points, you will get a clear visualization of how the function behaves for different values of [tex]\( x \)[/tex].
