To find the base of the logarithm when determining the inverse of [tex]\( 8^4 \)[/tex]:
1. First, understand that the inverse operation of exponentiation is taking the logarithm.
2. Specifically, if we have [tex]\( 8^4 \)[/tex], we want to determine the logarithm base that would allow us to revert to the initial input before exponentiation. In this case, it's asking for the base of this logarithm.
3. Mathematically, the inverse of [tex]\( 8^4 \)[/tex] can be expressed as [tex]\( \log_b(8^4) \)[/tex], where [tex]\( b \)[/tex] is the base of the logarithm. Because the base of the original exponential expression is 8, the logarithm must also use this base to invert it correctly.
Therefore, the base of the logarithm is:
[tex]\[ \boxed{8} \][/tex]
