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What is the solution to this equation?

[tex]\[ \ln (2x+4) = \ln (x+3) \][/tex]

A. [tex]\(x = 1\)[/tex]

B. [tex]\(x = -7\)[/tex]

C. [tex]\(x = -1\)[/tex]

D. [tex]\(x = 7\)[/tex]

Sagot :

GinnyAnsweridn
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]
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