To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 3^{2x+1} = 3^{x+5} \)[/tex], follow these steps:
1. Recognize that the bases on both sides of the equation are the same. Since the bases are identical and non-zero, the exponents must be equal for the equation to hold true. This leads us to:
[tex]\[
2x + 1 = x + 5
\][/tex]
2. To isolate [tex]\( x \)[/tex], first get all terms involving [tex]\( x \)[/tex] on one side of the equation and the constant terms on the other side. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
2x + 1 - x = x + 5 - x
\][/tex]
Simplifying this, we get:
[tex]\[
x + 1 = 5
\][/tex]
3. Next, solve for [tex]\( x \)[/tex] by isolating it. Subtract 1 from both sides:
[tex]\[
x + 1 - 1 = 5 - 1
\][/tex]
Simplifying this, we get:
[tex]\[
x = 4
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 4 \)[/tex]. The correct answer is:
[tex]\[
4
\][/tex]
