Not sure if I'm doing this right
Ln(3x-4)-Ln(x+1)=Ln(2)
My solution:
Ln 3x-4/x+1 =Ln2
3x-4/x+1=2/1
2x+2=3x-4
2=x-4
6=x
yes you are correct, but you must put brackets when typing in this format.
On paper you probably extend the fraction bar over the (x+1) but the way you typed it, it would be understood as
3x - 4/x + 1 as 3 separate terms on the left side
check out this reply
http://www.jiskha.com/display.cgi?id=1270500607
Your solution is correct! Let me explain the steps you took to solve the equation.
Step 1: Start by combining the logarithms on the left side of the equation using the properties of logarithms. The property you used is Ln(a) - Ln(b) = Ln(a/b).
So, Ln(3x-4) - Ln(x+1) = Ln(2) becomes Ln((3x-4)/(x+1)) = Ln(2).
Step 2: Since the logarithmic functions are equal, you can equate the expressions inside the logarithms. This gives you (3x-4)/(x+1) = 2.
Step 3: Next, you cross multiply to eliminate the fraction by multiplying both sides of the equation by (x+1), which gives you (3x-4) = 2(x+1).
Step 4: Simplify the equation by distributing on both sides. You get 3x - 4 = 2x + 2.
Step 5: Combine like terms by subtracting 2x from both sides and adding 4 to both sides. This simplifies the equation to x = 6.
So, your final solution is x = 6.