Answer :
To solve the equation [tex]\(2^{x-1} - 7 = 9\)[/tex], follow these steps:
1. Add 7 to each side of the equation:
[tex]\[
2^{x-1} - 7 + 7 = 9 + 7
\][/tex]
Simplifying gives:
[tex]\[
2^{x-1} = 16
\][/tex]
2. Write 16 as a power of 2:
We know that [tex]\(16\)[/tex] can be expressed as [tex]\(2^4\)[/tex]. So, we equate:
[tex]\[
2^{x-1} = 2^4
\][/tex]
3. Since the bases are the same, set the exponents equal to each other:
[tex]\[
x - 1 = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Add 1 to both sides:
[tex]\[
x = 4 + 1
\][/tex]
Simplifying gives:
[tex]\[
x = 5
\][/tex]
Therefore, the solution to the equation [tex]\(2^{x-1} - 7 = 9\)[/tex] is [tex]\(x = 5\)[/tex].
1. Add 7 to each side of the equation:
[tex]\[
2^{x-1} - 7 + 7 = 9 + 7
\][/tex]
Simplifying gives:
[tex]\[
2^{x-1} = 16
\][/tex]
2. Write 16 as a power of 2:
We know that [tex]\(16\)[/tex] can be expressed as [tex]\(2^4\)[/tex]. So, we equate:
[tex]\[
2^{x-1} = 2^4
\][/tex]
3. Since the bases are the same, set the exponents equal to each other:
[tex]\[
x - 1 = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Add 1 to both sides:
[tex]\[
x = 4 + 1
\][/tex]
Simplifying gives:
[tex]\[
x = 5
\][/tex]
Therefore, the solution to the equation [tex]\(2^{x-1} - 7 = 9\)[/tex] is [tex]\(x = 5\)[/tex].
