Predicting number of digits with logarithms

  • Thread starter Kartik.
  • Start date
  • #1
55
1
If log103 =0.477 then the number of digits in 340 will be?

100.477 = 3
10(0.47740)=340
hm...?
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
36,175
6,794
if log103 =0.477 then the number of digits in 340 will be?

100.477 = 3
10(0.47740)=340
hm...?

340 = (100.477)40 = 100.477*40
 
  • #3
chiro
Science Advisor
4,790
132
If log103 =0.477 then the number of digits in 340 will be?

100.477 = 3
10(0.47740)=340
hm...?


Hey Kartik and welcome to the forums.

Using log laws, we know that we wish to find log_10(3^40) which gives us the number of decimal digits required to represent 3^40.

Using log laws we first apply log_10(3^40) = 40log_10(3). Now you are given log_10(3), but in future if you wish to find log_b(x) where b is not the natural base e you use the relatioship log_b(x) = ln(x)/ln(b) where ln(x) is the natural logarithm of x and ln(b) must be non-zero (i.e. b can't be 1 or close enough to it for practical purposes).
 

Related Threads on Predicting number of digits with logarithms

Replies
8
Views
21K
  • Last Post
Replies
5
Views
2K
  • Last Post
2
Replies
32
Views
6K
Replies
5
Views
959
  • Last Post
Replies
14
Views
4K
  • Last Post
Replies
11
Views
22K
  • Last Post
Replies
15
Views
2K
Replies
8
Views
7K
Replies
8
Views
678
Top