how do u solve?

Question

ln(x-1) - ln(x) =ln(3)

Answer 1

By property of logarithm in quotient:
Ln(X-1) – Ln(X) = Ln(3)
Ln[(X-1)/X] = Ln(3)

(X-1)/X = 3
X-1 = 3X
-1 = 2X ====> X= -1/2

Answer 2

Take the e-power of the whole equation. The logarithms disappear, and the subtraction becomes division:
... (x - 1)/x = 3.

Solve this the "normal" way:
... (x - 1)/x = 3.
... x - 1 = 3 x
... -2x = 1
... x = -1/2.

The problem is, however, that you can't take logarithms of negative numbers. Therefore there are no solutions.

You could have seen this immediately from the fact that ln(x-1) is always less than ln(x), so that the left hand side of the equation is negative. However, ln(3) is positive, so there is no solution.

Answer 3

Ln ( x ) - Ln (y) = ln (x/y).........take taht into consideration

so

ln(x-1) - ln(x) = ln( (x-1) / x)

ln (( x-1)/x) = ln 3
take the inverse of ln to both sides which is e^......it cancles out the ln

(x-1)/ x = 3
x-1 = 3x
-1 = 2x
x= -1/2


*********
here is the problem

you can't take the natural log of a number less than 0....
x = -1/2 is less than zero.

Although when you combine the equation as mentioend above...you get a value for x........there is no value for x

no solution

Answer 4

a property of logarithms is the the difference of two logarithms is the logarithm of the quotient of their contents

so, ln(x-1)-ln(x)=ln[(x-1)/x)]

now, raise e to the power of both sides
the e and the ln cancel each other out

you get:

(x-1)/x=3
x-1=3x
2x=-1
x=-1/2

now you have to check by plugging this in to the original equation

ln(-1/2-1)-ln(-1/2)=? ln(3)

you can't have ln of a negative number so x=-1/2 doesn't work

so, there are no solutions

Answer 5

No Solution, since a has to be greater than 0 in ln (a)

We know ln (a) - ln (b) = ln (a/b)
so
ln(x-1) -ln (x) = ln 3
ln ((x-1)/x) = ln 3 : raise e both side
(x-1)/x=3
x-1=3x
-1=2x
x=-1/2

since x=-1/2 both ln( x -1 ) and ln (x) will be no solution

Answer 6

ln(x-1) - ln(x) = ln (3)
=> ln {(x-1)/x} = ln (3)
=> (x-1)/x = 3
=> x-1 = 3x
=> 2x = -1
=> x = (-1/2) or (-0.5)

Answer 7

ln(x-1) - ln(x) =ln(3)
ln(x-1)/x) = ln 3
(x-1)/x = 3
x-1 = 3x
-1 = 2x
x = -1/2
No solution possible

Answer 8

ln(x-1)/x = ln(3)...............ln(x) - ln(y) = ln(x/y)
(x-1)/x = 3......................remove ln
x - 1 = 3x
2x = -1
x = -1/2

Answer 9

ln((x-1)/x)=ln3
then you could say
((x-1)/x)=3
then you have

x-1=3x
then2x=-1
and
x=-1/2

Answer 10

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