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Section 8: Additional Topics

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 8.8 Additional Topics 861 Version: Fall 2007 8.8 Additional Topics Computing Large Powers Logarithms were originally used to compute large products and powers. Prior to the age of calculators and computers, mathematics students spent many hours learning and practicing these procedures. In current times, most of these computations can be done easily on a calculator, so the original use of logarithms is usually not taught anymore. However, calculators are still limited. They cannot compute large powers such as 253 789 (try it!), and most computer programs can’t either (all such tools have a limit on the size of the computations they can perform). So how can we compute large powers such as these? The idea is to use our knowledge of the properties of logarithmic and exponential functions. Here is the procedure: 1. First, let y = 253 789 , and take the log of both sides: log( y ) = log(253 789 ) = 789 log(253) (property of logs) 1896 . 062091 (calculator approximation) 2. Now the idea is to exponentiate both sides, using the function 10 x . However, your calculator still cannot compute 10 1896
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