Find the solution of this equation:
x^1/4 = 1400 * logx
2006-09-06 10:06:19 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Iam sure that this is correct
2006-09-06 10:26:38 · update #1
x^1/4 = 1400 * log x
Raising power 4 times
( x^1/4)^4 = (1400 * log x)^4
x = (1400)^4 (log x)^4
Taking log both sides
log x = 4 log 1400 + 4 log (log x)
log x - 4 log(logx) =12.58451214
let log x =t
t -4 log t = 12.58451214
Put t=17.56 then
LS=17.56 - 4(log 17.56)
=17.56 -4(1.244524512)
= 17.56 -4.978098046
=12.58190195 which is nearly equal
Hence t = 17.56 approximately
log x = 17.56
Therefore x =e^17.56=291239.7103
x = 291240 approximately
2006-09-06 10:36:53 · answer #1 · answered by Amar Soni 7 · 0⤊ 0⤋
Such this type of problems can never be solved analytically.
It is solved by graph or by the numerical method
For example:
You can use the recurrent relation
x(n+ 1)^1/4 = 1400 * logx(n)
(where x(n +1) is (subscript n +1) and x(n) is x subscript n)
now
1. choose some value for x1
2. Put n = 1 in the above equation you will get x2
3. Put n = 2 you will get the relation between x3 and x2, which enables you to get the the value of x3
and so on. after some steps you Will find that the value you get is very close to the input one. This will be the approximate solution
2006-09-14 15:23:19 · answer #2 · answered by Hassan g 2 · 0⤊ 0⤋
x = (1400* log x) ^4
2006-09-06 17:19:47 · answer #3 · answered by nondescript 7 · 0⤊ 0⤋
are you sure you got the equation right? I'm not sure this is easily solvable
2006-09-06 17:21:49 · answer #4 · answered by Scott S 2 · 0⤊ 0⤋
the answer doent exsist dumby
2006-09-06 17:37:28 · answer #5 · answered by Alana. 3 · 0⤊ 0⤋