Finding unknown indices

  • Thread starter malco97
  • Start date
  • #1
malco97
9
0
I would be grateful if someone could tell me how to find unknown indices.

e.g 3^x=9

(i know it is 2 but i would like to know the process for use with larger numbers).

Thankyou in advance
 

Answers and Replies

  • #2
enslam
11
0
3^x=9
therefore
9=3^2
get the log base 3 of both sides
x=2
 
  • #3
Lonewolf
337
1
No, you used the fact x=2.

9 = 3^x

log 9 = log (3^x)

log 9 = x log 3

x = log9/log3 = 2

log can be to any base as long as they are the same. you will usually find base 10, or base e on your calculator. log base e is usually ln.
 
  • #4
KLscilevothma
322
0
No, you used the fact x=2.

1) 3x=9
As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam.

here are more examples (solve for x)
2) 5x = 625
3) 4*5x = 100
4) 2x = 8

If you use Logarithm, in the step log9/log3, you need to know the fact that 9 = 3^2 too, unless you use a caculator.
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,021
970
1) 3x=9
As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam.

That's true as long as the "opposite" problem, finding the power, can be done easily- as long as the answer is an integer as in all of your examples.

To solve, for example 3x= 7, you will need to use logarithms.
 

Suggested for: Finding unknown indices

  • Last Post
Replies
1
Views
900
Replies
28
Views
2K
Replies
4
Views
894
  • Last Post
Replies
3
Views
985
  • Last Post
Replies
1
Views
875
Replies
1
Views
192
Replies
1
Views
1K
MHB Indices
  • Last Post
Replies
3
Views
1K
Replies
1
Views
331
  • Last Post
Replies
10
Views
852
Top