Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Also tell the functional relationship y= 

**Problem Statement:** When \(\log y\) is graphed as a function of \(x\), a straight line results. Graph a straight line, given by two points, on a log-linear plot, and determine the functional relationship. (The original x-y coordinates are given). Points: - \((x_1, y_1) = (-1, 1)\) - \((x_2, y_2) = (1, 5)\) **Task:** Graph a straight line on a log-linear plot. **Graph Options:** 1. **Graph A:** - X-axis: Ranges from -4 to 10. - Y-axis: Shows values as 1, 2, 4, 6, 8, 10. - The line is increasing steadily from near the bottom left towards the top right, indicating a positive slope. 2. **Graph B:** - X-axis: Ranges from -4 to 10. - Y-axis: Displays logarithmic values (base 10): \(10^0, 10^2, 10^4, 10^6, 10^8, 10^{10}\). - The line is increasing steadily, forming a straight positive slope on the logarithmic scale. 3. **Graph C:** - X-axis: Ranges from -4 to 10. - Y-axis: Displays logarithmic values (base 10): \(10^0, 10^2, 10^4, 10^6, 10^8, 10^{10}\). - The line is decreasing from top left to bottom right, indicating a negative slope. 4. **Graph D:** - X-axis: Ranges from -4 to 10. - Y-axis: Shows values as 1, 2, 4, 6, 8, 10. - The line is decreasing, moving from the top left to the bottom right, indicating a negative slope. The goal is to determine which graph represents the functional relationship between \(x\) and \(\log y\) such that the plotted data points form a straight line indicating the correct linear relationship in a log-linear context.
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Transcribed Image Text:**Problem Statement:** When \(\log y\) is graphed as a function of \(x\), a straight line results. Graph a straight line, given by two points, on a log-linear plot, and determine the functional relationship. (The original x-y coordinates are given). Points: - \((x_1, y_1) = (-1, 1)\) - \((x_2, y_2) = (1, 5)\) **Task:** Graph a straight line on a log-linear plot. **Graph Options:** 1. **Graph A:** - X-axis: Ranges from -4 to 10. - Y-axis: Shows values as 1, 2, 4, 6, 8, 10. - The line is increasing steadily from near the bottom left towards the top right, indicating a positive slope. 2. **Graph B:** - X-axis: Ranges from -4 to 10. - Y-axis: Displays logarithmic values (base 10): \(10^0, 10^2, 10^4, 10^6, 10^8, 10^{10}\). - The line is increasing steadily, forming a straight positive slope on the logarithmic scale. 3. **Graph C:** - X-axis: Ranges from -4 to 10. - Y-axis: Displays logarithmic values (base 10): \(10^0, 10^2, 10^4, 10^6, 10^8, 10^{10}\). - The line is decreasing from top left to bottom right, indicating a negative slope. 4. **Graph D:** - X-axis: Ranges from -4 to 10. - Y-axis: Shows values as 1, 2, 4, 6, 8, 10. - The line is decreasing, moving from the top left to the bottom right, indicating a negative slope. The goal is to determine which graph represents the functional relationship between \(x\) and \(\log y\) such that the plotted data points form a straight line indicating the correct linear relationship in a log-linear context.
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How does the second to last step come about? How does "log(5^x/2) + log(5^1/2)" turn into "log (sq. rt of 55^x)?"

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How does the second to last step come about? How does "log(5^x/2) + log(5^1/2)" turn into "log (sq. rt of 55^x)?"

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