SOLUTION: Need to know how to solve ln(x/3+1)+ln(1/x)=2

Question 958171: Need to know how to solve ln(x/3+1)+ln(1/x)=2
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Need to know how to solve ln(x/3+1)+ln(1/x)=2
-----------
Adding logs --> multiply

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
ln(x/3+1)+ln(1/x)=2
assuming x is positive, use logarithm product rule and we have
ln ( (x/3 + 1) * (1/x) ) = 2
ln (1/3 + 1/x ) = 2
use definition of logarithms
1/3 + 1/x = e^2
1/x = e^2 - 1/3
1/x = (3e^2 - 1) / 3
cross multiply fractions
(3e^2 - 1)*x = 3
x = 3 / (3e^2 - 1)

RELATED QUESTIONS
I need to solve ln(x)=... (answered by rapaljer)
how to solve:... (answered by lwsshak3)
please help - not sure how to solve when I end up with log fractions? ln(x)- ln(x+1) = (answered by longjonsilver)
Use logarithmic differentiation to solve: f(x) =(x^(3/2)*e^(-(x^2)))/(1-e^(x)) Don't (answered by jim_thompson5910)
how do I solve... (answered by stanbon)
Ln(x-1)+Ln(x+3)=Ln5 Cannot figure out how to solve, please... (answered by solver91311,RAY100)
Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)
How do you solve ln x + ln x^2=5 to get e^2... (answered by htmentor)
how do you solve ln(x)... (answered by Fombitz)