Logarithms
2011-09-20 18:13:00   来源：liuxuepaper.Com    双击单词自动翻译

　　In this case, it will take roughly 20.5 years for the town’s population to exceed 1500. So about halfway through the year 2021, the population will first exceed 1500.　　The general form for a problem like this one, in which the exponent is unknown, is to isolate the exponential term, take the logarithm of both sides, and then use the power rule of logarithms to bring the variable out of the exponent. You can then isolate the variable on one side of the equation. The base of the logarithms is insignificant. You could choose a base-10 logarithm or a logarithm of any other base, as long as it is consistently used.　　Here’s a simple example to illustrate this process:

　　If 6x = 51000, then find the value of x.

　　This problem would be vastly more difficult if we didn’t have logarithms. How would you possibly calculate 51000 anyhow? And how do you solve for x when it’s the exponent of a number? But by taking the logarithm of each side of the equation, and utilizing the power rule of logarithms:

　　The confusion clears, and we see that we have a logarithm problem that can be methodically solved.

（责任编辑：申月月）