College

To solve the equation [tex]$2^{x-1} - 7 = 9$[/tex], follow these steps:

1. Add 7 to each side:
[tex]$2^{x-1} = 16$[/tex]

2. Express 16 as a power of 2:
[tex][tex]$16 = 2^4$[/tex][/tex]

3. Set the exponents equal to each other:
[tex]$x-1 = 4$[/tex]

4. Solve for [tex]x[/tex]:
[tex]$x = 5$[/tex]

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].