Question

the solution of the equation $2^{x - 1}-7 = 9$ is $x = \square$.

Explanation:

Step1: Isolate the exponential term

Add 7 to both sides.
$2^{x-1} - 7 + 7 = 9 + 7$
$2^{x-1} = 16$

Step2: Rewrite right side as power of 2

Express 16 as $2^4$.
$2^{x-1} = 2^4$

Step3: Equate exponents (same base)

Set exponents equal since bases match.
$x - 1 = 4$

Step4: Solve for x

Add 1 to both sides.
$x = 4 + 1$

Answer:

$5$