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Chapter 8: Problem 2

Write a MATLAB program to generate a table of the base-10 logarithms between 1 and 10 in steps of \(0.1\). The table should start on a new page, and it should include a title describing the table and row and column headings. This table should be organized as shown below.

Short Answer

Expert verified
Here's the short answer based on the step-by-step solution: To create a MATLAB program that generates a table of base-10 logarithms from 1 to 10 in steps of 0.1, we'll use the following code: ``` % Create an array of numbers from 1 to 10 with a step size of 0.1 X = linspace(1, 10, 91); % Calculate the base-10 logarithms of the numbers in the array logValues = log10(X); % Print title and column headers fprintf('\n\nBase-10 logarithm table from 1 to 10\n'); fprintf('-------------------------------------\n'); fprintf(' Number Logarithm\n'); % Display the table with the desired format for i = 1:length(X) fprintf('%6.2f %9.6f\n', X(i), logValues(i)); end ``` This code creates an array of numbers from 1 to 10, calculates their base-10 logarithms, and then organizes and displays the results in a table as specified in the question.

Step by step solution

01

Create an array of numbers from 1 to 10 with a step size of 0.1

To create an array of numbers from 1 to 10 with a step size of 0.1, we can use the built-in MATLAB function `linspace()`. The syntax of this function is `linspace(start, end, num_points)` where `start` is the starting value, `end` is the ending value and `num_points` is the number of equally spaced points between the start and end values. In our case, we want a step size of 0.1, so we will have 91 equally spaced points between 1 and 10 as follows: `X = linspace(1, 10, 91);`
02

Calculate the base-10 logarithms of the numbers in the array

To calculate the base-10 logarithms of the numbers in the array `X`, we can use the MATLAB function `log10()` which computes the element-wise base-10 logarithm of the input array. The syntax for this function is `log10(X)` where X is an array of numbers. In our case, we will apply the `log10()` function to our array `X` and store the result in a new array called `logValues` as follows: `logValues = log10(X);`
03

Create the table with the desired format

To create a table with the desired format in MATLAB, we can use the following functions and commands: 1. `table(X, logValues, 'VariableNames', {'Numbers', 'Logarithms'})`: This creates a table with two columns, `Numbers` and `Logarithms`, and fills them with the values from the array `X` and `logValues`, respectively. 2. `display(T)`: This displays the table created by the `table()` function in the MATLAB command window. Here is how we can create the table in our MATLAB code: `T = table(X, logValues, 'VariableNames', {'Numbers', 'Logarithms'}); display(T);`
04

Add the title and organize the output

To add the title and organize the output, we can use the `fprintf()` function. This function allows us to include a custom title, column headers, and page breaks. In our case, we will add a title, row, and column headers using the following commands: ``` fprintf('\n\nBase-10 logarithm table from 1 to 10\n'); fprintf('-------------------------------------\n'); fprintf(' Number Logarithm\n'); ``` To display the table, we can make use of the `fprintf()` function again within a loop that iterates through the table and prints out each row: ``` for i = 1:length(X) fprintf('%6.2f %9.6f\n', X(i), logValues(i)); end ```
05

Final MATLAB code

Here is the complete MATLAB code that accomplishes the given task: ``` % Step 1: Create an array of numbers from 1 to 10 with a step size of 0.1 X = linspace(1, 10, 91); % Step 2: Calculate the base-10 logarithms of the numbers in the array logValues = log10(X); % Step 4: Add the title and organize the output fprintf('\n\nBase-10 logarithm table from 1 to 10\n'); fprintf('-------------------------------------\n'); fprintf(' Number Logarithm\n'); % Step 3: Display the table with the desired format T = table(X, logValues, 'VariableNames', {'Numbers', 'Logarithms'}); for i = 1:length(X) fprintf('%6.2f %9.6f\n', X(i), logValues(i)); end ```

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