Let's solve the equation:
[tex]\[
\ln(2x + 4) = \ln(x + 3)
\][/tex]
Since the natural logarithm function [tex]\(\ln\)[/tex] is one-to-one, we can equate the arguments of the logarithms:
[tex]\[
2x + 4 = x + 3
\][/tex]
Next, we need to solve for [tex]\(x\)[/tex]:
1. Subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
2x + 4 - x = x + 3 - x
\][/tex]
This simplifies to:
[tex]\[
x + 4 = 3
\][/tex]
2. Subtract 4 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x + 4 - 4 = 3 - 4
\][/tex]
This simplifies to:
[tex]\[
x = -1
\][/tex]
So, the solution to the equation [tex]\(\ln(2x + 4) = \ln(x + 3)\)[/tex] is:
[tex]\[
x = -1
\][/tex]
Hence, the correct answer is:
C. [tex]\(x = -1\)[/tex]
