2007-12-07 17:59:30 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let logs be to base 10 : -
log ( x / (x + 3) ) = 1
x / (x + 3) = 10^1
x = 10x + 30
9 x = - 30
x = - 10/3
2007-12-08 02:34:25 · answer #1 · answered by Como 7 · 3⤊ 3⤋
You are correct.
You can change it to: log { x / (x + 3) } = 1 and then, if you raise 10 to each side's value, you have:
x / (x + 3) = 10
x = 10x + 30
9x = -30
x = -30/9 = -10/3
If you then try substituting the answer back in to either log term in the original expression, you find yourself taking a log of a negative number. Which cannot be.
For instance, if {log(10) (-10/3)} is possible, then 10 to some power, say "n", can equal -10/3. But no power of 10 can equal a number equal to or less than zero.
So the answer can't work and is excluded, leaving no answer. This happens in the same fashion as in problems for which you obtain an answer, only to find it leaves you dividing by zero somewhere in the original or an interim expression.
So you are correct, it doesn't really have an answer.
2007-12-08 02:12:20 · answer #2 · answered by bimeateater 7 · 2⤊ 3⤋
log x - log (x+3)=1
log(x/(x+3)) = 1
x/x+3 = 10
x= 10x+30
9x = -30
x=-10/3
2007-12-08 02:12:14 · answer #3 · answered by MTG G 2 · 0⤊ 4⤋
log(x) - log(x + 3) = 1
log(x/(x + 3)) = 1
x/(x + 3) = 10
x = 10x + 30
-9x = 30
x = (-10/3) or -3 1/3
however, since you can't have a negative value inside the parenthesis
ANS : No Solution
2007-12-08 02:25:14 · answer #4 · answered by Sherman81 6 · 0⤊ 6⤋
log(x/(x+3)) =1
10^1=(x/(x+3))
10(x+3)=x
10x + 30 =x
9x = -30
x=- 3.333333333
sorry forgot a step .
you check this in your equation
log(-3.333333) there is no log negative
Log(-3.3333333+3) = log(-0.33333333) there is no log negative .
Therefore you are right , it has no solution.
2007-12-08 02:10:21 · answer #5 · answered by Murtaza 6 · 0⤊ 4⤋
Which base are you taking logs from? In any case, if you include complex numbers, there is definitely an answer. In fact, there are infinite answers. If you are only restricting yourself to real numbers, then there are no answers.
2007-12-08 02:42:16 · answer #6 · answered by The Prince 6 · 0⤊ 4⤋
log x - log (x+3) = 1
log(x/(x+3))=1
x/(x+3)=10^1
x/(x+3)=10
x=10x+30
-30=10x-x
-30=9x
x=-(30/9)
x=-(10/3)
x= -3 1/3
It does...
2007-12-08 02:10:07 · answer #7 · answered by hameerabbasi 3 · 2⤊ 5⤋
I think log x- log (x+3)=log ((x)/(x+3))=1
In which case, x = -10/3
Yes I'm right:
log (x/y) = logb x - logb y
2007-12-08 02:13:22 · answer #8 · answered by Anonymous · 0⤊ 5⤋
my logarithms are rusty. x=-10/3?
2007-12-08 02:11:43 · answer #9 · answered by mmatt314 3 · 0⤊ 4⤋
your right, it is a false equation. are you sure you didnt mean to subtract that 3?
2007-12-08 02:07:28 · answer #10 · answered by pyr032486 2 · 0⤊ 5⤋