sp08_152_Ch5_06_print

sp08_152_Ch5_06_print - Logarithm as Integral Oguz Kurt...

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Logarithm as Integral Oguz Kurt OSU-Math 152 Spring 2008 Oguz Kurt (OSU-Math 152) Logarithm as Integral Spring 2008 1 / 11
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Logarithm as an Integral Question: For positive real numbers a, b , how can we find a solution to the equation a x = b ? Namely, Find log a b =? Say we wish to solve 2 x = 5 . Namely, log 2 5 =? We know 2 2 = 4 < 5 and 2 3 = 8 > 5 .So, 2 < x < 3 . Try 2 2 . 5 = 5 . 65685424949 > 5 . So, 2 < x < 2 . 5 One way is to try the number in the middle of the last interval (for example, trying 2 . 25 and so on) till you get close enough to the perfect answer. However, finding the answer to our problem through this method is very hard and time-consuming. Not a very efficient method Oguz Kurt (OSU-Math 152) Logarithm as Integral Spring 2008 2 / 11
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Scottish Mathematician Napier used a different method while he invented logarithm as the first time in early 17th Century. He found the integer powers of 1 . 001 for a set of reasons: 1 it’s easy to calculate its powers 1 . 001 2 = 1
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This note was uploaded on 04/07/2008 for the course MATH 152 taught by Professor Kurt during the Spring '08 term at Ohio State.

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sp08_152_Ch5_06_print - Logarithm as Integral Oguz Kurt...

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