- #1

- 48

- 0

eg.. what is ? log (base 10) of 1381.42?? (without a calulator)??

- Thread starter jenzao
- Start date

- #1

- 48

- 0

eg.. what is ? log (base 10) of 1381.42?? (without a calulator)??

- #2

- 48

- 0

(with caveat that i memorized log 1 - 9)

- #3

lurflurf

Homework Helper

- 2,432

- 132

since

log(ab)=log(a)+log(b)

numbers should be decomposed multiplicatively.

One method is to factor into primes

log(1381.42)=-2+log(2)+2log(17)+log(239)

This shows a problem logs of many primes will be needed

another method would involve writing the number as a product of factors with known logs and factors near 1 since when x is small

log(1+x)~log(e)[x-x^2/2+x^3/3-x^4/4+...]

say one knew log(138176)

then

log(1381.42)=-2+log(138176)-log(1+1/4064)

- #4

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

First, log(1381.42)= log(0.138142 x10

Now, use the 'Taylor's Polynomial' expansion:

for 0< x< 1, log(x)= x+ (1/2)x

- Last Post

- Replies
- 15

- Views
- 10K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 20K

- Last Post

- Replies
- 9

- Views
- 9K

- Last Post

- Replies
- 11

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 13K

- Last Post

- Replies
- 1

- Views
- 7K

- Last Post

- Replies
- 6

- Views
- 14K

- Last Post

- Replies
- 6

- Views
- 1K