ln 12 - ln(x - 1) = ln(x-2)?

Question

solve for x, and PLEASE explain!!!

Answer 1

take ln(x-1) to the other side it beomes + and + is equal to in * in ln..

ln 12= ln [(x-1)(x-2)]

12 = (x-1)(x-2)

solving x as a quadratic equation gives u the answer as 5 and -2

Answer 2

This action needs no explanation:

ln 12 = ln(x-2) + ln(x-1)

now, remember that ln ab = ln a + ln b ?

ln 12 = ln [(x-2)(x-1)]

12 = (x-2)(x-1), this is a quadratic,

but you can look at it and see how to solve 12 =4*3, so...

one solution is x =5. Ignore the negative solution.

Answer 3

Using the laws of ln, ln(12)-ln(x-1) can be rewritten as ln(12/(x-1)).

Then take each side to e, so you get 12/(x-1)=x-2.

Then multiply each side by (x-1) to get 12=(x-2)(x-1).

After some expansion and such, you get 0=(x^2)-3x-10.

Using factorization, 0=(x+2)(x-5). Therefore, x=-2 and x=5. But, all ln have to be a non-negative number, therefore x=5.

Answer 4

ln(12/x-1)=ln(x-2)
12=x^2-3x+2
0=x^2-3-10
0=(x-5)(x+2)
x=5 bc u ignore the negative

Answer 5

ln 12 = ln(x-2) + ln (x-1) = ln (x-2) (x-1)

go to exponential e^lnx = x

(x-2) (x-1) =12

x^2 -3x +2 =12

x^2 -3x -10 =0

roots are 5 and -2 which is impossible since there are no ln of negative numbers

ANSWER x = 5

Answer 6

ln 12 - ln (x-1) = ln (x-2)
=> 12 / (x-1) = x-2
=> x^2 -3x -10 = 0
=> x^2 -5x +2x -10 = 0
=> x(x-5)+2(x-5) = 0
=> (x-5)(x+2)=0
x=5 OR x=-2

Answer 7

right here's a sprint: the 1st 2 words are the two squared and have an analogous variable ln(x). for this reason, 3ln(x)^2 could be subtracted from 5ln(x)^2 providing you with the hot equation 2ln(x)^2+a million=0. i'm not sure if which will help or no longer, even though it a minimum of simplifies your equation slightly.