solve: ln x - ln (x-1) = 2 and ln 6 + ln x - ln 2 = 3 and 4lny - ln3=5?

Question

for the first one .. I got up to x/x-1 = e^2 and then I kinda got stuck =.=;; Please Help! - Thank you

these are 3 separate equations - separated with the word and.

Answer 1

ln x - ln (x-1) = 2
<=> ln x = ln(x-1) + 2
<=> ln x = ln[(x-1)*e^2]
<=> x = (x-1)e^2 and x > 0
<=> x (1 - e^2) = -e^2 and x > 0
<=> x = e^2 / (e^2 -1)
ln 6 + ln x - ln 2 = 3
<=> ln x = 3 - ln3
<=> ln x = ln (e^3 /3)
<=> x = (e^3) /3
4lny - ln3=5
<=> ln y^4 = ln (3e^5) and y > 0
<=> y^4 = 3e^5
<=> y = sqrt (sqrt (3e^5))

Answer 2

ln (x + a million) - ln (3 - x) = ln (2 - x) Use your guidelines or lows of logs in coping with ln ln ((x+a million) /(3 -x )) = ln (2 - x) This states that (x + a million) /(3 - x) = (2 - x) Multiply both part by technique of (3 -x) (x + a million) = (2 - x)(3 - x) Multiply it out (x + a million) = x^2 - 5x + 6 rearrange right into a common quadratic equation x^2 - 6x + 5 = 0 (x - 5)(x - a million) = 0 x = 5 can't be used because (2 - 5) = -3 and also you won't be able to the ln of a detrimental huge style x = a million is the in effortless words answer

Answer 3

remember ln a -ln b = ln(a/b)

ln x-ln (x-1 = ln (x/(x-1)) =2 and x = (x-1) e^2

x = e^2 x -e^2 ---> x(e^2-1) = e^2

X = e^2/e^2-1 as e^2 = 7.39/6.39= 1.16

ln6 +lnx -ln 2 =3

lnx +ln (6/2) = 3 --->lnx = 3-ln3 =1.9

x = e^1.9 =6.7

4 ln y -ln 3 =5 ---> 4ln y = 5+ln 3 = 6.1 lny = 1.52

y=4.6