Question

4^{7 - x} = 256

Explanation:

Step1: Express 256 as a power of 4

We know that \(4^4 = 256\), so the equation \(4^{7 - x}=256\) can be rewritten as \(4^{7 - x}=4^4\).

Step2: Set the exponents equal

Since the bases are the same and the exponential function \(y = 4^x\) is one - to - one (if \(a^m=a^n\) where \(a>0,a
eq1\), then \(m = n\)), we can set the exponents equal to each other: \(7 - x=4\).

Step3: Solve for x

Subtract 7 from both sides of the equation: \(-x=4 - 7=-3\).
Multiply both sides by - 1: \(x = 3\).

Answer:

\(x = 3\)