sp08_152_Ch5_06_print

# sp08_152_Ch5_06_print - Logarithm as Integral Oguz Kurt...

This preview shows pages 1–4. Sign up to view the full content.

Logarithm as Integral Oguz Kurt OSU-Math 152 Spring 2008 Oguz Kurt (OSU-Math 152) Logarithm as Integral Spring 2008 1 / 11

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 11

sp08_152_Ch5_06_print - Logarithm as Integral Oguz Kurt...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online