SOLUTION: In(x+3)-In(3x)=0

Question 1148870: In(x+3)-In(3x)=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

note: those uppercase "i"s should be the letter "L" instead. The notation Ln or LN refers to the natural log. It's unfortunate that the lowercase "L" looks almost identical to uppercase "i".

Log Rules:
1. Ln(x) - Ln(y) = Ln(x/y)
2. If Ln(x) = y, then x = e^y

Let's solve for x:
Ln(x+3) - Ln(3x) = 0
Ln[(x+3)/(3x)] = 0 ... use rule 1
(x+3)/(3x) = e^0 ... use rule 2
(x+3)/(3x) = 1
x+3 = 1(3x) .... multiply both sides by 3x
x+3 = 3x
x+3-x = 3x-x ... subtract x from both sides
3 = 2x
2x = 3
2x/2 = 3/2 ... divide both sides by 2
x = 3/2
x = 1.5

The answer as a fraction is x = 3/2
In decimal form, that is equivalent to x = 1.5

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