Question

The solution of the equation \( 2^{x+2} + 2^{x+1} = 48 \) will be:

• A. \( x = 2 \)
• B. \( x = 4 \)
• C. \( x = 3 \)
• D. \( x = 5 \)

Hint:

When solving exponential equations, try to factor out common terms and equate the exponents of the same base.

Answer 1

The Correct Option is C

Given the equation: \[ 2^{x+2} + 2^{x+1} = 48 \] Step 1: Factor out the common term \( 2^{x+1} \) from both terms on the left-hand side: \[ 2^{x+1}(2 + 1) = 48 \] \[ 2^{x+1} \times 3 = 48 \] Step 2: Divide both sides of the equation by 3: \[ 2^{x+1} = \frac{48}{3} \] \[ 2^{x+1} = 16 \] Step 3: Since \( 16 = 2^4 \), we can equate the exponents: \[ x+1 = 4 \] Step 4: Solve for \( x \): \[ x = 4 - 1 \] \[ x = 3 \]