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

Question

?(1 point)
Responses

x=54
x equals Start Fraction 5 over 4 End Fraction

x=−34
x equals negative Start Fraction 3 over 4 End Fraction

x=43
x equals Start Fraction 4 over 3 End Fraction

x=34

Answer 1

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

\[ 3 = 12 - 12x \]

Next, we can solve for \( x \):

1. Subtract 12 from both sides:

\[ 3 - 12 = -12x \]

\[ -9 = -12x \]

2. Divide both sides by -12:

\[ x = \frac{-9}{-12} = \frac{9}{12} = \frac{3}{4} \]

Therefore, the solution to the equation \( \ln(3) = \ln(12 - 12x) \) is:

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

None of the provided options seem to match \( x = \frac{3}{4} \). Please double-check your options. If you have more information or possible answers, let me know!