Which of the following correctly solves the equation ln(3)=ln(12−12x)

Question

?(1 point)
Responses

x=4/3
x equals Start Fraction 4 over 3 End Fraction

x=−3/4
x equals negative Start Fraction 3 over 4 End Fraction

x=5/4
x equals Start Fraction 5 over 4 End Fraction

x=3/4

Answer 1

To solve the equation \( \ln(3) = \ln(12 - 12x) \), we can use the property of logarithms that states if \( \ln(a) = \ln(b) \), then \( a = b \).

So we can set the arguments equal to each other:

\[ 3 = 12 - 12x \]

Now, let's solve for \( x \):

1. Subtract 12 from both sides: \[ 3 - 12 = -12x \] \[ -9 = -12x \]

2. Divide both sides by -12: \[ x = \frac{-9}{-12} = \frac{9}{12} = \frac{3}{4} \]

So, the solution to the equation is:

\[ x = \frac{3}{4} \]

The correct response is:

x equals Start Fraction 3 over 4 End Fraction