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SAT2数学考试题目:Logarithms

2019-09-23 16:33:00来源:网络

  为了帮助大家高效备考SAT,新东方在线SAT频道为大家带来SAT2数学考试题目:Logarithms,希望对大家SAT备考有所帮助。更多精彩尽请关注新东方在线SAT频道!

  Logarithms have important uses in solving problems with complicated exponential equations. Consider the following example:

  The population of a small town is 1000 on January 1, 2001. It grows at a constant rate of 2% per year. In what year does the population of the town first exceed 1500?

  This question is like the exponential growth problems we’ve just seen but with a twist. Here, we’re given the growth rate, the initial quantity, and the ending quantity. We need to find the number of percent changes (in this case, the number of years) that links all these values. Since logarithms are the power to which you must raise a given number to equal another number, they are the perfect tool for solving this sort of problem.

  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.

  以上就是关于“SAT2数学考试题目:Logarithms”的内容,更多精彩内容,请关注SAT频道!


本文关键字: SAT数学 SAT

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