SOLUTION: Solve the logarithmic equation. ln(3x-1)=ln5-ln(x-5)

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Question 363142: Solve the logarithmic equation.
ln(3x-1)=ln5-ln(x-5)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
ln%283x-1%29=ln%285%29-ln%28x-5%29
ln%283x-1%29=ln%285%2F%28x-5%29%29
3x-1=5%2F%28x-5%29
%283x-1%29%28x-5%29=5
3x%5E2-15x-x%2B5=5
3x%5E2-16x=0
x%283x-16%29=0
Two solutions:
highlight%28x=0%29
.
.
.
3x-16=0
3x=16
highlight%28x=16%2F3%29
.
.
.
However, since x=0 would lead to a negative argument for the natural log function it is not allowed as a solution.
highlight_green%28x=16%2F3%29