Answer :

GinnyAnswer
Let's solve the given equation step-by-step:

The equation given is
[tex]\[ \log_2(3x - 7) = 3. \][/tex]

To solve for [tex]\(x\)[/tex], we can convert the logarithmic equation into an exponential equation. Recall the property that [tex]\(\log_b(a) = c\)[/tex] implies [tex]\(a = b^c\)[/tex]. In this case, [tex]\(b = 2\)[/tex], [tex]\(a = 3x - 7\)[/tex], and [tex]\(c = 3\)[/tex]. Therefore, we can rewrite the equation as:

[tex]\[ 3x - 7 = 2^3. \][/tex]

We know that:
[tex]\[ 2^3 = 8. \][/tex]

So the equation becomes:
[tex]\[ 3x - 7 = 8. \][/tex]

Next, we solve for [tex]\(x\)[/tex]. First, add 7 to both sides of the equation to isolate the term involving [tex]\(x\)[/tex]:

[tex]\[ 3x - 7 + 7 = 8 + 7, \][/tex]
which simplifies to:
[tex]\[ 3x = 15. \][/tex]

Now, divide both sides by 3 to solve for [tex]\(x\)[/tex]:

[tex]\[ x = \frac{15}{3}. \][/tex]

This simplifies to:

[tex]\[ x = 5. \][/tex]

So the solution to the equation [tex]\(\log_2(3x - 7) = 3\)[/tex] is:

[tex]\[ x = 5. \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{5}. \][/tex]

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