若函数y=lg|ax-1|的图象关于x=2对称，则非零实数a=______．
设P点为函数y=lg|ax-1|的图象上任一点，其坐标为（x0，y0），
则y0=lg|ax0-1|，且P点关于x=2的对称点坐标为（4-x0，y0），
又由函数y=lg|ax-1|的图象关于x=2对称，则必有y0=lg|a（4-x0）-1|
故y0=lg|ax0-1|=lg|a（4-x0）-1|，即|ax0-1|=|a（4-x0）-1|，亦即|ax0-1|=|-ax0+4a-1|
由于上式对任意的实数x0均成立，故4a-1=1，即a=1 2
故答案为 1 2
Loneliness is all about feeling isolated, but it's actually quite common. In general, there are three different types of loneliness. The first kind of loneliness is temporary. It is the most common type but usually disappears quickly and does not require any special attention. The second kind, situational loneliness, is a natural result of a particular situation, such as, family problem, the death of a loved one, or moving to a new place. Although this kind of loneliness can cause physical problems, it usually does not last for more than a year. The third kind of loneliness is chronic (the opposite of “temporary”). Being the most severe, it usually lasts for more than two years and is often connected with serious illnesses. An important factor in loneliness is a person’s social contacts. Through social contacts, we get emotional support and guidance from our parents and teachers and share similar interests and activities with our friends. However, some lonely people almost make no contacts with people around them and feel apart from those who they supposedly know well. They just see themselves as outsiders. On the other hand, some lonely people may have enough social contacts, but they rarely enjoy the contacts and question their popularity, thinking of themselves as someone powerless. So loneliness is closely related to the quality of those social relationship in addition to the quantity. Loneliness is tough, but something can be done to cope with it. First, take time to accept that you are suffering from loneliness. Then, contact your old friends or visit relatives to spend quality time with others. Besides, pick up a hobby to reduce your feelings of loneliness, such as taking up needle work, joining craft classes, or attending lectures. You can also beat loneliness by volunteering at a nursing home, hospital, church or pet rescue organization. This not only helps you get in touch with people from all walks of life, but also makes you feel good about yourself. In a word, if you take a correct attitude towards loneliness and get involved with people around you, you are sure to get over it.
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