To solve the equation [tex]\(3^{2x + 1} = 3^{x + 5}\)[/tex], we can make use of the property of exponents that states if the bases are the same, then the exponents must be equal.
Given:
[tex]\[3^{2x + 1} = 3^{x + 5}\][/tex]
Since the bases are identical (base 3), we can set the exponents equal to each other:
[tex]\[2x + 1 = x + 5\][/tex]
Now, we solve for [tex]\(x\)[/tex]:
1. Subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[2x + 1 - x = x + 5 - x\][/tex]
Simplifying, we get:
[tex]\[x + 1 = 5\][/tex]
3. Subtract 1 from both sides:
[tex]\[x + 1 - 1 = 5 - 1\][/tex]
Simplifying, we get:
[tex]\[x = 4\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(4\)[/tex].
Thus, the correct answer is:
[tex]\[4\][/tex]
