SOLUTION: How do you work out the percentage increase/decrease between two figures? Example. What is the percent increase/decrease from 41210 to 38853?

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Question 4281: How do you work out the percentage increase/decrease between two figures?
Example. What is the percent increase/decrease from 41210 to 38853?
Found 2 solutions by khwang, AnlytcPhil:
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Use loga x = 1/logx a to change the base.

(loga x * logb x)/(loga x +logb x)
= (1/logx a) * (1/logx b) / ( 1/logx a + 1/logx b)
= (1/(logx a * logx b) / [(logx a + logx b)(logx a * logx b)]
= 1/(logx a + logx b)
= 1/logx ab
= logab x

Kenny

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that:
(logax·logbx)/(logax + logbx) =logabx
`
We must assume that a, b, and x are all positive
and different from 1, otherwise the above is not defined.
`
We need two rules of logarithms
(1) logmn = 1/lognm, when m and n are positive but neither is 1
(2) logmp + logmq = logm(pq), when m,p,q are positive and m is not 1
`
Use (1) to replace every term in left hand side 

      1         1
   ------- · -------
    logxa     logxb
-----------------------
    1          1
 ------- + --------
  logxa      logxb


Multiply top and bottom by logxa·logxb


        1
--------------------
 logxb + logxa
 
      1
------------
  logx(ba)
 


` use (1)

       1
 ------------
       1
   --------
    logbax
 

     logbax

     logabx

Edwin