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2. Property of Logarithms: Since the natural logarithm function is one-to-one, if [tex]\(\ln A = \ln B\)[/tex], then [tex]\(A = B\)[/tex]. Therefore, we can equate the arguments of the logarithms: [tex]\[
2x + 4 = x + 3
\][/tex]
3. Solve for [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we will subtract [tex]\(x\)[/tex] from both sides of the equation: [tex]\[
2x + 4 - x = x + 3 - x
\][/tex] Simplifying both sides, we get: [tex]\[
x + 4 = 3
\][/tex]
4. Further Simplifying: Subtract 4 from both sides: [tex]\[
x + 4 - 4 = 3 - 4
\][/tex] [tex]\[
x = -1
\][/tex]
5. Verify the Solution: Substitute [tex]\(x = -1\)[/tex] back into the original equation to ensure it is correct: [tex]\[
\ln(2(-1) + 4) = \ln((-1) + 3)
\][/tex] [tex]\[
\ln(2 - 2) = \ln(2)
\][/tex] [tex]\[
\ln(2) = \ln(2)
\][/tex] Both sides are equal, confirming that [tex]\(x = -1\)[/tex] is indeed a solution.
### Conclusion
The solution to the equation [tex]\(\ln(2x + 4) = \ln(x + 3)\)[/tex] is: [tex]\[
\boxed{x = -1}
\][/tex]
Thus, the correct answer is: [tex]\[
\boxed{\text{B. } x = -1}
\][/tex]
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