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## Sagot :

Step-by-step:

1.

**Understanding the Logarithmic Equation:**

The given equation is [tex]\(\log_3(x + 5) = 2\)[/tex]. A logarithm is the inverse of an exponentiation. Specifically, [tex]\(\log_b(a) = c\)[/tex] means that the base [tex]\(b\)[/tex] raised to the power of [tex]\(c\)[/tex] equals [tex]\(a\)[/tex].

2.

**Convert to Exponential Form:**

The equation [tex]\(\log_3(x + 5) = 2\)[/tex] can be rewritten in its exponential form as follows:

[tex]\[ 3^2 = x + 5 \][/tex]

This step uses the property that if [tex]\(\log_b(a) = c\)[/tex], then [tex]\(b^c = a\)[/tex].

3.

**Rewrite the Equation:**

Simplify [tex]\(3^2\)[/tex]. We know that:

[tex]\[ 3^2 = 9 \][/tex]

Hence, the equation [tex]\(3^2 = x + 5\)[/tex] simplifies to:

[tex]\[ 9 = x + 5 \][/tex]

4.

**Shifting Terms:**

To isolate [tex]\(x\)[/tex], we subtract 5 from both sides of the equation:

[tex]\[ 9 - 5 = x \][/tex]

Simplifying further gives:

[tex]\[ 4 = x \][/tex]

Among the provided options, the equivalent equation to [tex]\(\log_3(x + 5) = 2\)[/tex] is:

[tex]\[ 3^2 = x + 5 \][/tex]

Therefore, the correct answer is:

[tex]\[ 3^2 = x + 5 \][/tex]