Solve the equation.
-ln (60) - ln x = ln (x - 4)
A) -6
B) 32
C) 10, -6
D) 10

Question

Quizplus · Accepted Answer

Using the properties of logarithm, we can simplify the equation as:

ln(60/x) = ln(x-4)

Now, we can solve for x by equating the arguments of the logarithmic function:

60/x = x-4

Expanding the equation, we get:

x^2 - 4x - 60 = 0

Factoring the quadratic equation, we get:

(x - 10)(x + 6) = 0

Therefore, the solutions to the equation are x = 10 and x = -6. However, since we cannot take the natural logarithm of a negative number, the only valid solution is x = 10.

Thus, the answer is D.

Solve the Equation. -Ln (60) - Ln X = Ln (X - 4)