To solve for [tex]\( x \)[/tex] in the equation [tex]\( (-2)^x = 256 \)[/tex], let's break down the steps:
1. Understanding the bases and exponents:
- We need to express [tex]\( 256 \)[/tex] as a power of [tex]\( -2 \)[/tex]. Notice that [tex]\( 256 \)[/tex] is a positive number, and we know that a negative base raised to an even power results in a positive number.
2. Express [tex]\( 256 \)[/tex] as a power of 2:
- We know that [tex]\( 256 = 2^8 \)[/tex].
3. Considering the negative base:
- Since [tex]\( -2 \)[/tex] is our base, we need to figure out the exponent such that [tex]\( (-2)^x = 256 \)[/tex].
- Observe that [tex]\( (-2)^8 \)[/tex] would equal [tex]\( (-2)^8 = (2^8) = 256 \)[/tex] because raising -2 to an even power results in a positive value, specifically [tex]\( 256 \)[/tex] in this case.
4. Identifying the exponent:
- Given that [tex]\( (-2)^8 = 256 \)[/tex], we can conclude that [tex]\( x = 8 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( (-2)^x = 256 \)[/tex] is [tex]\( \boxed{8} \)[/tex].
