To solve the equation [tex]\(\log_8(x) = 0\)[/tex], we can use properties of logarithms and exponents.
1. Recall the definition of a logarithm: If [tex]\(\log_b(a) = c\)[/tex], then [tex]\(b^c = a\)[/tex].
2. In our case, the given equation is [tex]\(\log_8(x) = 0\)[/tex]. This means that [tex]\(8\)[/tex] raised to the power of [tex]\(0\)[/tex] is equal to [tex]\(x\)[/tex].
3. Mathematically, this can be expressed as:
[tex]\[
8^0 = x
\][/tex]
4. We know that any non-zero number raised to the power of [tex]\(0\)[/tex] is equal to [tex]\(1\)[/tex]. Therefore:
[tex]\[
8^0 = 1
\][/tex]
5. Thus, we have:
[tex]\[
x = 1
\][/tex]
Hence, the value of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
