Sure, let's solve the equation [tex]\(2^x = 32\)[/tex] step-by-step.
1. Understand the equation: The given equation is [tex]\(2^x = 32\)[/tex]. This means we need to find the value of [tex]\(x\)[/tex] such that when 2 is raised to the power of [tex]\(x\)[/tex], the result is 32.
2. Express 32 as a power of 2: We know that 32 can be written as a power of 2. Let's recall the powers of 2:
[tex]\[
2^1 = 2, \quad
2^2 = 4, \quad
2^3 = 8, \quad
2^4 = 16, \quad
2^5 = 32
\][/tex]
We see that 32 is equal to [tex]\(2^5\)[/tex].
3. Set the exponents equal to each other: Since [tex]\(2^x = 32\)[/tex] and [tex]\(32 = 2^5\)[/tex], we have:
[tex]\[
2^x = 2^5
\][/tex]
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[
x = 5
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(5\)[/tex].
