Question

Ln(x+4) - ln(x+3)=ln 3

Answer 1

Ln((x+4)/(x+3)) = ln3
(x+4)/(x+3)=3
x+4=3(x+3)
x+4=3x+9
2x=-5 ⇒ x=-2,5

Answer 2

To solve the equation ln(x+4) - ln(x+3) = ln(3), we can use logarithmic properties and simplify the equation.

First, we can combine the logarithms on the left side using the quotient rule of logarithms, which states that ln(a) - ln(b) = ln(a/b). Applying this rule to our equation, we have:

ln((x+4)/(x+3)) = ln(3)

Now, we can remove the natural logarithm from both sides by taking the exponential of both sides. The exponential function e^x and the natural logarithm ln(x) are inverse functions, so they cancel each other out. Applying the exponential function to both sides, we get:

e^(ln((x+4)/(x+3))) = e^(ln(3))

Simplifying further, the exponential function and the natural logarithm cancel each other out, and we are left with:

(x+4)/(x+3) = 3

Next, we can cross-multiply to get rid of the fraction:

(x+4) = 3(x+3)

Expanding the right side:

x + 4 = 3x + 9

Now, we can solve this equation for x. Subtracting x from both sides:

4 = 2x + 9

Subtracting 9 from both sides:

-5 = 2x

Dividing both sides by 2:

x = -5/2

Therefore, the solution to the equation ln(x+4) - ln(x+3) = ln(3) is x = -5/2.