Find value of \( X \) \( x^{X}=256 \)

To solve the equation \( x^X = 256 \), we recognize that \( 256 \) can be expressed as a power of \( 2 \): \( 256 = 2^8 \). Thus, we can rewrite the equation as: \[ x^X = 2^8 \] Now, we can explore the possibilities for \( x \) and \( X \). If we set \( x = 2^k \) (where \( k \) is a positive integer), we can substitute into the equation: \[ (2^k)^X = 2^8 \] This simplifies to: \[ 2^{kX} = 2^8 \] From this point, we can equate the exponents: \[ kX = 8 \] Now we can find various pairs of \( (k, X) \) that satisfy this equation. For example, if \( k = 1 \), then \( X = 8 \); if \( k = 2 \), then \( X = 4 \); and if \( k = 4 \), then \( X = 2 \). Therefore, the equation \( x^X = 256 \) can have multiple solutions depending on the chosen values of \( x \) and \( X \). Ultimately, to find \( X \) uniquely, you'd need specific constraints or additional equations!