Problem: Article: According to the second property of logarithms, known as the "quotient rule," the logarithm of a quotient can be rewritten by subtracting the logarithm of the denominator from the logarithm of the numerator. Written as an equation: logb(m / n) = logb(m) - logb(n) Also note that the following must be true: m > 0 n > 0 Before you can solve the logarithm, you need to shift all logs in the equation to one side of the equal sign. The other parts of the equation should all be shifted to the opposite side of the equation. Use inverse operations to accomplish this. Example: log3(x + 6) = 2 + log3(x - 2) log3(x + 6) - log3(x - 2) = 2 + log3(x - 2) - log3(x - 2) log3(x + 6) - log3(x - 2) = 2 If there are two logarithms in the equation and one must be subtracted by the other, you can and should use the quotient rule to combine the two logarithms into one. Example: log3(x + 6) - log3(x - 2) = 2 log3[(x + 6) / (x - 2)] = 2 Now that there is only one logarithm in the equation, use the logarithms definition to rewrite the equation in exponential form, thereby removing the log. Example: log3[(x + 6) / (x - 2)] = 2 Comparing this equation to the definition [y = logb (x)], you can conclude that: y = 2; b = 3; x = (x + 6) / (x - 2) Rewrite the equation so that: by = x 32 = (x + 6) / (x - 2) With the equation now in exponential form, you should be able to solve for x as you usually would. Example: 32 = (x + 6) / (x - 2) 3 * 3 = (x + 6) / (x - 2) 9 = (x + 6) / (x - 2) 9 * (x - 2) = [(x + 6) / (x - 2)] * (x - 2) 9x - 18 = x + 6 9x - x - 18 + 18 = x - x + 6 + 18 8x = 24 8x / 8 = 24 / 8 x = 3 Go back and double-check your steps. Once you feel certain that you have the correct solution, write it down. Example: x = 3
Summary: Know the quotient rule. Isolate the logarithm to one side of the equation. Apply the quotient rule. Rewrite the equation in exponential form. Solve for x. Write your final answer.

Problem: Article: Spend some time figuring out how your final grade will be calculated. This will help you to know what you should spend the most time on. For example, if 60% of your grade comes from exams, you should spend the majority of your work time studying for exams. On the other hand, if 60% of your grade comes from papers or other assignments, you should focus a large portion of your energy there. Calculate the scores you need to achieve on the remaining assignments to pass the class. You could even use an online calculator to help you figure this out, such as http://www.benegg.net/grade_calculator.html. In most college courses, this information should be spelled out in the syllabus. If your teacher hasn't provided this information for you in printed form or on a course website, don't hesitate to ask. Keep track of how well you are doing in each aspect of the class. This will give you a sense of whether or not you are passing, and again, where to focus your energies. Further, research shows that students who track their progress in class score better than those who do not. For example, if you do very well on coursework assignments, but are struggling with exams, you want to consider spending less time on the coursework and more time preparing for tests. Figure out what time of day you are most productive and energetic. Aim to dedicate that time to studying for the class you are struggling with. Create a routine in which you study for this class at the same time each day, and let your friends and family know you are unavailable during this period.
Summary: Learn how your grade will be calculated. Track your performance. Study when you are most productive.

Problem: Article: To let someone know you're interested in him, start by making eye contact. Move your eyes to his, hold briefly, then look away. Repeat this a few times,so that he knows you're intentionally looking at him. Don't stare at him. Staring is when you maintain fixed eye contact with someone for longer than a few seconds. Staring can seem aggressive or angry. Pair your eye contact with a slight smile. Make sure to watch his response. If he doesn't return your gaze, this is a sign he's not interested. If he looks back, smiles at you, or otherwise responds positively, that's a sign he's okay with your flirting. Lower your bottom lip slightly so your teeth are barely showing. You don't need to purse your lips, just open your mouth to entice the viewer. The pout is the first stage of the seductive lip bite. Studies show that women initiate flirting 90% of the time. Men flirt largely in response to feeling that flirtation has been initiated by women. A Manchester University study found that men spend the first 7 to 10 seconds of contact looking at women's lips before moving onto other areas. Once you've confirmed that he's interested, initiate the lip pout. Remember that not all cultures share the same body flirtation signals. Maintain eye contact while you pout your lips. After establishing eye contact, lowering your eyelids, or glancing at the object of your flirtation through your eyelashes, is a nonverbal indication of desire. You may want to lower your chin and look up at the person to strike a seductive pose. Some people find themselves naturally blinking their eyes more rapidly. This is also called "batting" the eyes. If this comes naturally to you, it can be another way to add your eyes to the flirtation. If it doesn't come naturally, it might seem like you have something stuck in your eye, and is best avoided. The downward tilt of the chin is said to make women look more "feminine" and flirtatious. Men, on the other hand, are said to look more "masculine" when they tilt their chin up and gaze slightly down their nose. Look at one eye, and then move to the other eye and down to the lips. This will draw his attention to your lips. The reason your eye gaze will draw his attention to your lips is through the tendency of one person to mirror, or imitate, another when engaged in flirtation. Directing your eye gaze to a man's lips is an overtly flirtatious gesture. It's a nonverbal way of indicating sexual interest. Bite tenderly on 1 side of the inner lip for 2 to 5 seconds, before slowly releasing. Maintain eye contact throughout. With eye contact, there's less chance that your lip bite could be misunderstood. Make sure your teeth don't bite your outer lip, as this may appear insecure or nervous. A seductive bite should be gentle, never hurtful. It should not leave a mark. Following your lip bite, you may want to add a slight lick of your lower lip with your tongue. Your tongue is a sexual body part, and using your tongue now will make your flirtatious overture more seductive. Don't overdo it with lip-licking. This can result in chapped lips, which is the opposite effect you are trying to achieve. Continue to make seductive eye contact throughout your encounter. The seductive lip bite is one gesture in the choreography of your flirtation, working together with others.
Summary:
Make eye contact. Start a lip pout and bite soon after you make eye contact. Lower your eyelashes seductively. Do a triangle gaze. Bring your lower lip in very slightly. Lick your lower lips.