The following table shows the area (in \text{km}^2) for 12 countries, using a \text{log} scale:
How many countries have an area between 10\,000 \text{ km}^2 and 100\,000 \text{ km}^2?
How many countries have an area between 10\,000 \text{ km}^2 and 1\,000\,000 \text{ km}^2?
| Log of area | Number of countries |
|---|---|
| 3 - 4 | 1 |
| 4 - 5 | 3 |
| 5 - 6 | 7 |
| 6 - 7 | 1 |
The following histogram has been plotted on a \log_{10} scale:
What is the total frequency of scores between 1 and 100?
What is the total frequency of scores larger than 0.1?
What is the total frequency of scores smaller than 10?
The lifespans of various animals and insects are shown in the table below:
| \text{Animal/Insect} | \text{Lifespan (days)} | \text{Lifespan in a } \log_{10} \text{ scale} |
|---|---|---|
| \text{Ant} | 20 | |
| \text{African elephant} | 25\,500 | 4.41 |
| \text{Bowhead whale} | 71\,400 | |
| \text{Bumblebee} | 21 | 1.32 |
| \text{Chicken} | 2920 | 3.47 |
| \text{Dog} | 5110 | |
| \text{Emperor penguin} | 8500 | 3.93 |
| \text{Fly} | 18 | |
| \text{Giraffe} | 10\,120 | |
| \text{Hamster} | 780 | 2.89 |
| \text{Ladybug} | 365 | |
| \text{Little penguin} | 2190 | 3.34 |
| \text{Monkey} | 7300 | |
| \text{Shark} | 10\,980 | 4.04 |
Complete the table by converting the lifespans to a \log_{10} scale, rounding each value to two decimal places. Some values have already been filled in.
Create a histogram to represent this data, on a \log_{10} scale.
The Richter Scale is a base 10 logarithmic scale used to measure the magnitude of an earthquake, given by R = \log_{10} x, where x is the relative strength of the quake. An earthquake that registers 4.0 on the Richter scale is 10 times stronger than an earthquake that measures 3.0. Some past earthquakes and their Richter scales are shown in the table below:
How many times stronger was the earthquake in Sumatra compared to the earthquake in China? Round your answer to the nearest whole number.
How many times stronger is a quake of 7.6 than one of 5.2? Round your answer to the nearest whole number.
| Earthquake | Richter scale |
|---|---|
| \text{Sumatra 2004} | 9.1 |
| \text{China 2008} | 7.9 |
| \text{Haiti 2010} | 7.0 |
| \text{Italy 2009} | 6.3 |
The aftershock of an earthquake measured 6.7 on the Richter Scale, and the main quake was 4 times stronger. Find the magnitude of the main quake on the Richter Scale, to one decimal place.
The Richter scale is used to measure the intensity of earthquakes. The formula for the Richter scale rating of a quake is given by R = \log \left(\dfrac{x}{a}\right), where a is the intensity of a minimal quake that can barely be detected, and x is a multiple of the minimal quake’s intensity.
The table shows how quakes are categorised according to their Richter scale rating.
| Minor | light | Moderate | Strong | |
|---|---|---|---|---|
| Richter rating | 2-3.9 | 4-4.9 | 5-5.9 | 6-6.9 |
A seismograph measures the intensity of a quake to be x = 5711 a. Determine the Richter scale rating R of this quake to one decimal place.
In which category does the quake fall?
The decibel scale, which is used to record the loudness of sound, is a logarithmic scale.
In the decibel scale, the lowest audible sound is assigned the value of 0.
A sound that is 10 times louder than 0 is assigned a decibel value of 10.
A sound 100 (10^{2}) times louder than 0 is assigned a decibel value of 20.
In general, an increase of 10 decibels corresponds to an increase in magnitude of 10. The table shows the decibel value for various types of noise:
How many times louder is the sound of industrial noise than the sound of a wind turbine?
If the sound of a normal speaking voice is 50 decibels, and the sound in a bus terminal is 80 decibels, then how many times louder is the bus terminal compared to the speaking voice?
| Type of noise | Decibel value |
|---|---|
| \text{Jet plane} | 150 |
| \text{Pneumatic drill} | 120 |
| \text{Industrial} | 110 |
| \text{Stereo music} | 100 |
| \text{Inside a car} | 90 |
| \text{Office} | 70 |
| \text{Houehold} | 60 |
| \text{Wind turbine} | 50 |
| \text{Bedroom} | 30 |
| \text{Falling leaves} | 20 |
A financial planner has clients with a large range of annual incomes. To manage the data more easily, the income (in dollars) of each client is first converted to a \log_{10} scale.
What income would result in 4.9 on a \log_{10} scale?
What range of incomes corresponds to a range of 5 to 6 on the \log_{10} scale?