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Question

ln(4x+6)-ln(x+5)=lnx

Answer 1

ln (4x+6) - ln (x+5) = ln x

or, ln (4x+6)/(x+5) = ln x

taking anti log (to base e) to both sides we get

(4x+6)/ (x+5) = x

or, 4x+6 = x(x+5) = x^2 +5x

or, - x^2 -5x+4x+6 = 0

or, - x^2 - x +6 =0

or, x^2 +x-6=0

or, x^2 +3x-2x-6=0

or x(x+3) -2(x+3)=0

or (x-2)(x+3)=0

or x = 2 and - 3

and that is answer

cool :)

Answer 2

cerdinalz is wrong.

subtraction in logs is division.

ln[(4x+6)/(x+5)] = lnx

THEN get rid of the lns:

(4x+6)/(x+5) = x
4x+6 = x(x+5) = x² + 5x
0 = x² +x + 6 = (x + 3)(x - 2)

and since you can't take the ln of a negative number, throw out the -3 and say x=2.

It's wrong to keep the -3, because if you plug it in the original equation, you get ln (-3), which is not allowed.

Answer 3

ln(4x+6) - ln(x+5) = Ln(x)
Move ln(x+5) to right side
ln(4x+6) = ln(x) + ln(x+5)
use property of logs, ln(a) + ln(b) = ln(ab) to rewite right side.
ln(4x+6) = ln(x(x+5))
raise both sides to power of e:
4x+6 = x(x+5)
4x+6 = x^2 + 5x
0 = x^2 + x - 6
use quadratic formula to solve
x = 2, x = -2, however the answer -2 can not be evaluated in ln(4x+6), so the only answer is 2.

Answer 4

ln[(4x+6)/(x+5)]=Ln x
(4x+6)/(x+5)=x
4x+6 = x(x+5)
4x+6=x^2+5x
x^2 + x - 6 = 0
(x-2)(x+3)=0
x=2 or x=-3
therefore x=2 (since ln -3 does not exist)

Answer 5

exp[ln(4x+6) - ln(x+5)] = exp[lnx] = x
exp[ln(4x+6)]exp[-ln(x+5)] = x
(4x+6)/(x+5) = x
Multiply both sides by (x+5):
4x + 6 = x^2 + 5x
x^2 + x - 6 = 0
(x+3)(x-2) = 0
x = -3, 2

Answer 6

ln[(4x+6)/x+5]=lnx
(4x+6)/(x+5)=x
4x+6=x(x+5)
4x+6=x^2+5x
x^2+x-6=0
(x+3)(x-2)=0
x=-3 or 2

Answer 7

since the base is all ln you can automatically make it
(4x+6)-(x+5)=x
then do basic algebra
2x=-1
x=-.5

Answer 8

ln(4x+6)-ln(x+5)=lnx
ln((4x+6)/(x+5))=ln x
((4x+6)/(x+5)=x
4x+6=x(x+5)=x^2+5x
x^2+5x-4x-6=0
x^2+x-6=0
(x+3)(x-2)=0
x+3=0
x=-3
x-2=0
x=2