Question

20 of 2320 of 23 Items








Question
Solve the logarithmic equation ln(3x−11)=ln(4+2x)
.(1 point)
x=

Answer 1

To solve the equation \( \ln(3x - 11) = \ln(4 + 2x) \), we can use the property that if \( \ln(a) = \ln(b) \), then \( a = b \). Thus, we set the arguments of the logarithms equal to each other:

\[
3x - 11 = 4 + 2x
\]

Now, we will solve for \( x \). Let's first isolate \( x \) by rearranging the equation:

1. Subtract \( 2x \) from both sides:
\[
3x - 2x - 11 = 4
\]
This simplifies to:
\[
x - 11 = 4
\]

2. Now, add \( 11 \) to both sides:
\[
x = 4 + 11
\]
Thus, we have:
\[
x = 15
\]

Now, we need to check if this solution is valid by substituting \( x = 15 \) back into the original arguments of the logarithm:

- For \( 3x - 11 \):
\[
3(15) - 11 = 45 - 11 = 34
\]

- For \( 4 + 2x \):
\[
4 + 2(15) = 4 + 30 = 34
\]

Both arguments are equal and positive, which means our solution is valid.

Therefore, the solution to the logarithmic equation is:
\[
\boxed{15}
\]