To solve the equation [tex]\(2^{7x - 3} = 16\)[/tex], follow these steps:
1. Express 16 as a power of 2:
Notice that 16 can be written as a power of 2: [tex]\(16 = 2^4\)[/tex].
2. Rewrite the equation:
Since [tex]\(2^{7x - 3} = 16\)[/tex] and [tex]\(16 = 2^4\)[/tex], you can equate the exponents of 2. This gives:
[tex]\[
7x - 3 = 4
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- Add 3 to both sides of the equation:
[tex]\[
7x - 3 + 3 = 4 + 3
\][/tex]
Simplifying this, you get:
[tex]\[
7x = 7
\][/tex]
- Divide both sides by 7:
[tex]\[
x = \frac{7}{7}
\][/tex]
Simplifying this, you get:
[tex]\[
x = 1
\][/tex]
So, the solution is [tex]\(x = 1\)[/tex].
Answer:
A. The solution is [tex]\(x = 1\)[/tex]
