How do you graph a logarithmic function?
Graphing Logarithmic Functions
- The graph of inverse function of any function is the reflection of the graph of the function about the line y=x .
- The logarithmic function, y=logb(x) , can be shifted k units vertically and h units horizontally with the equation y=logb(x+h)+k .
- Consider the logarithmic function y=[log2(x+1)−3] .
How do you reflect a logarithmic function?
A General Note: Reflections of the Parent Function y=logb(x)
- reflects the parent function y=logb(x) y = l o g b ( x ) about the x-axis.
- has domain (0,∞) , range, (−∞,∞) , and vertical asymptote x = 0 which are unchanged from the parent function.
How do you know if a graph is a logarithmic function?
Key Points
- When graphed, the logarithmic function is similar in shape to the square root function, but with a vertical asymptote as x approaches 0 from the right.
- The point (1,0) is on the graph of all logarithmic functions of the form y=logbx y = l o g b x , where b is a positive real number.
What’s the difference between logarithmic and exponential graphs?
The inverse of an exponential function is a logarithmic function. Remember that the inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.
How do you graph a natural logarithmic function?
The natural logarithmic function, y = loge x, is more commonly written y = ln x. The graph of the function defined by y = ln x, looks similar to the graph of y = logb x where b > 1. The characteristics of this new function are similar to logarithmic function characteristics we already know.
How do you do exponential graphs?
Graphing Exponential Functions
- Replacing x with −x reflects the graph across the y -axis; replacing y with −y reflects it across the x -axis.
- Replacing x with x+h translates the graph h units to the left.
- Replacing y with y−k (which is the same as adding k to the right side) translates the graph k units up.
What is difference between linear and logarithmic scale?
Linear graphs are scaled so that equal vertical distances represent the same absolute-dollar-value change. The logarithmic scale reveals percentage changes. A change from 100 to 200, for example, is presented in the same way as a change from 1,000 to 2,000.
What is a logarithmic function?
A logarithmic function is a function of the form. which is read “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1. There are no restrictions on y.
What is logarithmic function example?
Comparison of exponential function and logarithmic function
| Exponential function | Logarithmic function | Read as |
|---|---|---|
| 103 = 1000 | log 1000 = 3 | log base 10 of 1000 |
| 100 = 1 | log 1 = 0 | log base 10 of 1 |
| 252 = 625 | log 25 625 = 2 | log base 25 of 625 |
| 122 = 144 | log 12 144 = 2 | log base 12 of 144 |
What is the difference between a logarithmic function and an exponential function?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. So you see a logarithm is nothing more than an exponent.
Where do you use logarithms in real life?
Exponential and logarithmic functions are no exception! Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).
How do logarithms make our life easier?
For example, the (base 10) logarithm of 100 is the number of times you’d have to multiply 10 by itself to get 100. The simple answer is that logs make our life easier, because us human beings have difficulty wrapping our heads around very large (or very small) numbers.
What are logarithms good for?
It lets you work backwards through a calculation. It lets you undo exponential effects. Beyond just being an inverse operation, logarithms have a few specific properties that are quite useful in their own right: Logarithms are a convenient way to express large numbers.
What is the benefit of using a logarithmic scale?
Presentation of data on a logarithmic scale can be helpful when the data: covers a large range of values, since the use of the logarithms of the values rather than the actual values reduces a wide range to a more manageable size; may contain exponential laws or power laws, since these will show up as straight lines.
What is the use of logarithmic graph?
There are two main reasons to use logarithmic scales in charts and graphs. The first is to respond to skewness towards large values; i.e., cases in which one or a few points are much larger than the bulk of the data. The second is to show percent change or multiplicative factors.
Is the Richter scale logarithmic?
On Earth, the severity of an earthquake is measured by the amount of ground movement that it produces. The Richter Scale has been in use for many years and is an example of a logarithmic scale.
Is a 10.0 earthquake possible?
No, earthquakes of magnitude 10 or larger cannot happen. No fault long enough to generate a magnitude 10 earthquake is known to exist, and if it did, it would extend around most of the planet.
What is the Richter scale formula?
The Richter scale defines the magnitude of an earthquake to be R=log(IcIn) where Ic is the intensity of the earthquake and In is the intensity of a standard earthquake.
What is the max on the Richter scale?
In theory, the Richter scale has no upper limit, but, in practice, no earthquake has ever been registered on the scale above magnitude 8.6. (That was the Richter magnitude for the Chile earthquake of 1960. The moment magnitude for this event was measured at 9.5.).
Is a 4.5 earthquake strong?
Richter magnitudes. . Events with magnitudes greater than 4.5 are strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors are not located in the earthquake’s shadow. The following describes the typical effects of earthquakes of various magnitudes near the epicenter.
What is a 10 on the Richter scale?
The Richter scale is logarithmic so a force 10 is ten times stronger than 9 and 100 times stronger than 8. A magnitude 9.0 earthquake on Richter scale is equivalent to release of energy by 25,000 nuclear bombs. So a 10.0 magnitude earthquake will be analogous to dropping over 4,00,000 nuclear bombs at a time. …
How strong is a 2.4 earthquake?
More examples
| Approximate Richter Magnitude number | Seismic energy equivalent: Amount of TNT | Example event |
|---|---|---|
| 1.5 | 178kg | Bomb used in WWII |
| 2 | 1 metric ton | Large Bomb used in WWII |
| 2.5 | 5.6 metric tons | Blockbuster bomb (dropped from airplanes) in WWII |
| 3.5 | 178 metric tons | Chernobyl accident, 1986 |
Can you feel a 2.2 earthquake?
Normally, earthquakes below magnitude 3 or so are rarely felt. However, smaller quakes from magnitude 2.0 can be felt by people if the quake is shallow (few kilometers only) and if people are very close to its epicenter and not disturbed by ambient factors such as noise, wind, vibrations of engines, traffic etc.
What does a 9.0 earthquake feel like?
The shaking will feel violent and it will be difficult to stand up. The contents of your house will be a mess. A large earthquake far away will feel like a gentle bump followed several seconds later by stronger rolling shaking that may feel like sharp shaking for a little while.
What would a 10.0 earthquake do?
A magnitude 10.0 quake could occur if the combined 3,000 km of faults from the Japan Trench to the Kuril-Kamchatka Trench move by 60 meters, Matsuzawa said. A magnitude 10 quake would likely cause ground motions for up to an hour, with tsunami hitting while the shaking was still going on, according to the research.
Is a 12.0 earthquake possible?
The magnitude scale is open-ended, meaning that scientists have not put a limit on how large an earthquake could be, but there is a limit just from the size of the earth. A magnitude 12 earthquake would require a fault larger than the earth itself.