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# how do you solve ln(x+1)-ln(x)=ln4

ln(x+1)-ln(x)=ln4

### 2 Answers by Expert Tutors

Felice R. | Need Help in Math and Science - Engineer willing to helpNeed Help in Math and Science - Engineer...
4.0 4.0 (1 lesson ratings) (1)
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ln(x+1) -ln(x) = ln(4)

if you remember the basic rules of logs

1) logb(mn) = logb(m) + logb(n)

2) logb(m/n) = logb(m) – logb(n)

3) logb(mn) = n · logb(m)

So if we look at your eqn, we can use rule 2

ln(x+1) - ln(x) = ln((x+1)/x)) = ln 4

Then if you remember that to solve an eqn for a given variable you need to undo whatever has been done to the variable. In our case, utilizing the inverse of the ln(x)

f (f -1(x)) = eln(x) = x

we can apply that to both sides of the eqn

eln((x+1)/x)) = eln 4  ⇒  (x+1)/x = 4

then solving this for x is easier

(x+1)/x) = 4
(x+1)/x •  x = 4 • x
x+1 = 4x
x+1 -x = 4x -x
1 = 3x
1/3 = 3x/3
x = 1/3

Hope this helps
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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ln[(x+1)/x] = ln4
So, (x+1)/x = 4
x+1 = 4x