Question

If \(2^x+2^{x+1}=48\), then the value of \(x^x\) is

• A. 4
• B. 64
• C. 256
• D. 16

Answer 1

The Correct Option is C

To solve the equation \(2^x+2^{x+1}=48\), we begin by simplifying the expression. Notice that the term \(2^{x+1}\) can be rewritten as \(2 \cdot 2^x\). Thus, the equation becomes:

\(2^x + 2 \cdot 2^x = 48\)

This can be further simplified by factoring out \(2^x\):

\(2^x(1 + 2) = 48\)

Simplifying inside the parentheses gives:

\(2^x \cdot 3 = 48\)

Divide both sides by 3 to isolate \(2^x\):

\(2^x = \frac{48}{3} = 16\)

Since \(2^x = 16\) and recognizing that \(16 = 2^4\), we have \(x=4\). Now, we need to find the value of \(x^x\):

\(x^x = 4^4\)

Calculate \(4^4\):

\(4^4 = (4^2)^2 = 16^2 = 256\)

Therefore, the value of \(x^x\) is:

256