Question

solve the equation.
$2^{x - 3} = 16$
$x = ?$

Explanation:

Step1: Express 16 as a power of 2

Since \( 16 = 2^4 \), we can rewrite the equation \( 2^{x - 3}=16 \) as \( 2^{x - 3}=2^4 \).

Step2: Set exponents equal (since bases are same)

For exponential equations with the same base (\( a^m = a^n \) implies \( m = n \) when \( a>0,a
eq1 \)), we have \( x - 3 = 4 \).

Step3: Solve for x

Add 3 to both sides of the equation \( x - 3 = 4 \). So \( x=4 + 3=7 \).

Answer:

\( x = 7 \)