INPUT ARTICLE: Article: 102 is 100. 103 is 1000. The powers 2 and 3 are the base-10 logarithms of 100 and 1000. In general, ab = c can be rewritten as logac = b. So, saying "ten to the power of two is 100" is equivalent to saying "the base-ten log of 100 is two." Each logarithmic table is only usable with a certain base (a in the equation above). By far the most common type of log table uses base-10 logs, also called the common logarithm. Multiply two numbers by adding their powers. For example: 102 * 103 = 105, or 100 * 1000 = 100,000. The natural log, represented by "ln", is the base-e log, where e is the constant 2.718. This is a useful number in many areas of math and physics. You can use natural log tables in the same way that you use common, or base-10, log tables. Let's say you want to find the base-10 log of 15 on a common log table. 15 lies between 10 (101) and 100 (102), so its logarithm will lie between 1 and 2, or be 1.something. 150 lies between 100 (102) and 1000 (103), so its logarithm will lie between 2 and 3, or be 2.something. The .something is called the mantissa; this is what you will find in the log table. What comes before the decimal point (1 in the first example, 2 in the second) is the characteristic. This column will show the first two or, for some large log tables, three digits of the number whose logarithm you're looking up. If you're looking up the log of 15.27 in a normal log table, go to the row marked 15. If you're looking up the log of 2.57, go to the row marked 25. Sometimes the numbers in this row will have a decimal point, so you'll look up 2.5 rather than 25. You can ignore this decimal point, as it won't affect your answer. Also ignore any decimal points in the number whose logarithm you're looking up, as the mantissa for the log of 1.527 is no different from that of the log of 152.7. This column will be the one marked with the next digit of the number whose logarithm you're looking up. For example, if you want to find the log of 15.27, your finger will be on the row marked 15. Slide your finger along that row to the right to find column 2. You will be pointing at the number 1818. Write this down. For 15.27, this number is 7. Your finger is currently on row 15 and column 2. Slide it over to row 15 and mean differences column 7. You will be pointing at the number 20. Write this down. For 15.27, you will get 1838. This is the mantissa of the logarithm of 15.27. Since 15 is between 10 and 100 (101 and 102), the log of 15 must be between 1 and 2, so 1.something, so the characteristic is 1. Combine the characteristic with the mantissa to get your final answer. Find that the log of 15.27 is 1.1838.

SUMMARY: Understand what a logarithm is. Identify the characteristic of the number whose log you want to find. Slide your finger down to the appropriate row on the table using the leftmost column. On the appropriate row, slide your finger over to the appropriate column. If your log table has a mean difference table, slide your finger over to the column in that table marked with the next digit of the number you're looking up. Add the numbers found in the two preceding steps together. Add the characteristic.

INPUT ARTICLE: Article: If you have a spider infestation in your home, basic spider killer sprays can be purchased to treat the infection. These are usually used outside the home. You spray the perimeters of your home, as well as any cracks or crevices spiders may use to enter your house. Choose a spray at a local department store. You should know the basic build of your home before going in so you know what sprays are safe for your house. Go around the perimeter of your home. Spray around the house's foundation. Also, look for potential entryways for spiders. Pay special attention to cracks in windowsills and garage entryways. Specifics regarding safe use depend on the type of spray you're using. The bottle or package should provide safety instructions. Always read these carefully before using any spider sprays. If you're wary about using chemicals around your home, essential oils can help. Try creating a mixture using essential oils and see if you notice a difference. Spiders tend to dislike the taste of essential oils. You can purchase essential oils online or at a local health store. For best effect, use neem oil and tea tree oil. Mix about two tablespoons of dish soap into warm water. Then, add 5 drops of tea tree oil and an ounce of neem oil. Sprinkle this mixture around your home in areas where you've noticed spiders. Be careful, however. Make sure you do not leave the spray close to children or pets. Tea tree oil can be harmful if swallowed. There are a variety of insecticides you can use to ward off spiders. Stop by your local hardware store and review your options. Dust insecticides are best used if you're treating cracks and crevices. They can be easily applied to hard-to-reach places in your home. Powder insecticides work best for spot treatment. If you've only seen spiders in a few spots in your home, consider a powder insecticide. If you're trying to create a boundary around your home, look into a liquid insecticide. They are usually mixed with water and then used to cover large areas around the home. As always, make sure to carefully review safety instructions of any products you buy prior to use. Many people feel more comfortable with electronic repellants as they don't involve spraying your home. Electronic repellents generate electromagnetic waves that repel spiders and other pests. You can find them online or at a hardware store. Read product reviews carefully before making a purchase, however, to make sure the repellent works for most people. If you have a serious spider infestation, you may not be able to treat it on your own. In this case, you should hire a professional exterminator. You should be especially proactive about this if you live in an area where poisonous spiders are common.

SUMMARY: Try sprays. Use essential oils. Look into insecticides. Try out an electronic repellant. Get professional help, if necessary.

INPUT ARTICLE: Article: Motivating a cat isn't likely with praise. They don't work in a partnership, so there is no reason to really do what you command. When the cat sits, you can praise it, but be sure to do so with a treat as well. Cats do not respond well to dominance or stress. When stressed, they are likely act out, and they certainly won't be responsive to training. To avoid negative reactions from your cat, be sure not to react negatively to failure or setbacks. When your cat doesn't sit immediately, and it won't, remember the following: Do not punish. There is a good chance that no matter the punishment, your cat won't make an association between it and the action. If it doesn't sit and you punish it, there may be an association with any number of other things instead of your actual command. Do not get physical with the cat. Hitting, shaking, or slapping could make it fearful. If that happens, the cat may avoid you, which will make training nearly impossible. Do not force the issue. The more you force it, the more likely the cat will stress out. Cats learn on their own terms, and at different speeds. You may just frighten the cat if you push too hard. Use the treats solely for training. If you use the treats too often, your cat will start to beg. It will pester you for a treat when it does anything whatsoever. You will want to be on the ground with your cat to show you want its attention. It may also help because being higher than your cat could appear like you're about to pounce and show dominance. The extra focus should help when trying to persuade your cat to start the sitting movements.

SUMMARY:
Motivate with treats over praise. Be positive. Sit on the ground.