To solve the equation [tex]\(4^{2x + 1} = 4^5\)[/tex], we can follow these steps:
1. Identify the Bases:
Both sides of the equation have the same base, which is 4.
2. Equate the Exponents:
Since the bases are the same, the exponents must be equal for the equation to hold true. Therefore, we can set the exponents equal to each other:
[tex]\[
2x + 1 = 5
\][/tex]
3. Isolate the Variable [tex]\(x\)[/tex]:
Solve for [tex]\(x\)[/tex] by first isolating the term containing [tex]\(x\)[/tex]. Subtract 1 from both sides:
[tex]\[
2x + 1 - 1 = 5 - 1
\][/tex]
Simplifying this, we get:
[tex]\[
2x = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 2:
[tex]\[
x = \frac{4}{2}
\][/tex]
Simplifying this, we find:
[tex]\[
x = 2
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{2}\)[/tex].
