Solve the equation. $$ \begin{array}{c}2^{x-3}=16 \ x=[?]\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
2^{x-3} = 16
$$

follow these steps:

### Step 1: Express 16 as a Power of 2

First, recognize that 16 is a power of 2:

$$
16 = 2^4
$$

### Step 2: Set the Exponents Equal

Since the bases are the same (both are 2), you can set the exponents equal to each other:

$$
x - 3 = 4
$$

### Step 3: Solve for $$ x $$

Add 3 to both sides of the equation to isolate $$ x $$:

$$
x = 4 + 3
$$
$$
x = 7
$$

### Final Answer

$$
x = 7
$$
$$ x = 7 $$

Solve the equation. \[ \begin{array}{c}2^{x-3}=16 \\ x=[?]\end{array} \]