Using a CAS calculator, find \log_{10} 3828.3 correct to two significant figures.
Using a CAS calculator, find x if \log_{10} x = 0.6. Round your answer to two significant figures.
The number line below has a \log_{10} scale. Plot the number 100 on the scale below:
Evaluate \log_{10}40. Round your answer to two decimal places.
In order to estimate \log_{10}90 without a calculator:
Find \log_{10}10.
Find \log_{10}100.
Hence, which two integers does \log_{10}90 lie between?
The logarithm of which number is equal to zero?
Solve \log_{10}x = 3.2 for x. Round your answer to two decimal places.
Each number line below has a \log_{10} scale. For each number line, determine the value of the point plotted on the line. Round your answers to two significant figures.
The data in the table shows the population of 10 countries:
Using a spreadsheet on your CAS calculator calculate the \log_{10} of the population for each country.
Write the results in the table correct to three significant figures.
| \text{Country} | \text{Population} | \text{log}_{10}\text{ Population} |
|---|---|---|
| \text{Iran} | 80\,530\,288 | |
| \text{Poland} | 38\,577\,192 | |
| \text{Nepal} | 29\,032\,238 | |
| \text{Senegal} | 15\,840\,344 | |
| \text{Paraguay} | 6\,771\,929 | |
| \text{Georgia} | 3\,975\,869 | |
| \text{Honduras} | 8\,251\,664 | |
| \text{Bhutan} | 788\,839 | |
| \text{Malaysia} | 30\,974\,279 | |
| \text{Denmark} | 5\,702\,131 |
The data in the table shows the area (in square kilometres) of 10 countries:
Using a spreadsheet on your CAS calculator calculate the \log_{10} of the area for each country.
Write your results in the table correct to three significant figures.
| \text{Country} | \text{Area}\\ \left(\text{km}^2\right) | \text{log}_{10}\text{ Area} |
|---|---|---|
| \text{Egypt} | 1\,001\,450 | |
| \text{United Kingdom} | 244\,820 | |
| \text{Mozambique} | 801\,590 | |
| \text{Cambodia} | 181\,040 | |
| \text{Sierra Leone} | 71\,740 | |
| \text{Panama} | 78\,200 | |
| \text{Montenegro} | 14\,026 | |
| \text{Croatia} | 56\,542 | |
| \text{Malaysia} | 329\,750 | |
| \text{Lebanon} | 10\,400 |
The histogram below shows the weights (in kilograms) of 26 zoo animals plotted on a log scale:
A monkey has a weight of 45.8\text{ kg}. What is the \log_{10} of 45.8 correct to two significant figures?
What weight (in \text{kg}) does the number - 2 represent on the log weights scale?
How many animals have a weight of at least 1000\text{ kg}?
What percentage of animals have a weight less than 0.1 \text{ kg}? Round your answer to two significant figures.
How many animals have a weight of at least 0.1\text{ kg} but less than 100\text{ kg}?
The histogram below shows the income (in dollars) of 24 employees plotted on a log scale:
A employee has an income of \$46\,974. What is the \log_{10} of 46\,974 correct to two significant figures?
What income does the number 5 represent on the log-income scale?
How many people have an income of at least \$10\,000?
What percentage of people have an income less than \$100\,000?
How many people have an income of at least \$10\,000 but less than \$10\,000\,000?
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?
The table below lists the oil production in barrels per day for 20 countries:
| \text{Country} | \text{Oil Production}\\ \text{(barrels per day)} | \text{log}_{10}\text{ Oil Production} |
|---|---|---|
| \text{Saudi Arabia} | 10\,625\,000 | |
| \text{China} | 3\,938\,000 | |
| \text{Norway} | 1\,763\,000 | |
| \text{India} | 736\,000 | |
| \text{Ecuador} | 555\,000 | |
| \text{Thailand} | 265\,000 | |
| \text{Brunei} | 113\,000 | |
| \text{Uzbekistan} | 85\,000 | |
| \text{France} | 61\,000 | |
| \text{Peru} | 39\,000 | |
| \text{Albania} | 21\,000 | |
| \text{Croatia} | 18\,000 | |
| \text{Belgium} | 13\,000 | |
| \text{Finland} | 13\,700 | |
| \text{Portugal} | 7100 | |
| \text{Bangladesh} | 4800 | |
| \text{Japan} | 4000 | |
| \text{Lativia} | 1150 | |
| \text{Costa Rica} | 300 | |
| \text{Zambia} | 200 |
Using your CAS calculator, calculate the \log_{10} value of each countries oil production to complete the table.
Construct a frequency histogram of log oil production.
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 |
Convert the lifespans to a \log_{10} scale to complete the table, 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 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 given histogram shows the area (in square kilometres) for 12 countries, plotted using a log scale:
How many countries have an area of between 10\,000\text{ km}^2 and 100\,000\text{ km}^2?
The histogram shows the masses (in grams) of a group of insects and animals, plotted on a \log_{10} scale:
How many animals and insects are included in the data altogether?
A caterpillar has a mass of 3 grams. What value does this take on a \log_{10} scale? Round your answer to two decimal places.
Which interval on the histogram would include a cat that has a mass of 4.5\text{ kg}?
From the data in the histogram, how many of the animals or insects had a mass that was over 100 grams?
