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=43
x equals Start Fraction 4 over 3 End Fraction

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

x=−34

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 \( a = b \). This leads us to the following equation:

\[ 3 = 12 - 12x \]

Next, we will solve for \( x \). Subtract 12 from both sides:

\[ 3 - 12 = -12x \]

This simplifies to:

\[ -9 = -12x \]

Now, divide both sides by -12:

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

Thus, the correct solution is:

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

So the correct response from the options provided is:

x equals Start Fraction 3 over 4 End Fraction