New! Section 1.4 – Graphing with Emphasis on Semilog and Double-log plots
Instructions
- The following videos were recorded specifically for MATH 147.
- The first videos below explain the concepts in this section.
- This page also includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.
Concepts
- Explaining the logarithmic scale
- Graphing double-log plots
- Graphing semilog plots
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Solve the following:
- Use logarithms to transform \(y=76x^{0.92}\), \(x\in \mathbb{R}\) to a linear function.
- Transform \(y=76x^{0.92}\), \(x\in \mathbb{R}\) to a linear function on a double-log plot.
- Graph \(y=76x^{0.92}\) on a double-log plot.
- \(Y=\log(76)+0.92X\)
- \(Y=\log(76)+0.92X\)
- See the video for the graph.
2. Consider the points \((x_1,y_1)=(1,2)\) and \((x_2,y_2)=(10,83.8)\) on a double log plot. Write a non-linear function to represent the graph containing these two points
\(y=2x^{\log(41.9)}\)
3. Solve the following:
- Use logarithms to transform \(y=103\cdot(0.943)^x,\) \(x\in \mathbb{R}\) to a linear function.
- Transform \(y=103\cdot(0.943)^x,\) \(x\in \mathbb{R}\) to a linear function on a semilog plot.
- Graph \(y=103\cdot(0.943)^x\) on a semilog plot.
- \(Y=\log(103)+x\log(0.943)\)
- \(Y=\log(103)+x\log(0.943)\)
- See the video for the graph.
4. Write a non-linear function to represent the line graphed on the semilog plot.
\(y=\dfrac{1}{10}\cdot 10^{\frac{7}{10}x}\)