Sure, let's solve the equation [tex]\(\log_8(x) = 1\)[/tex].
1. The given equation is [tex]\(\log_8(x) = 1\)[/tex].
2. To find [tex]\(x\)[/tex], we need to convert the logarithmic equation to its exponential form. The general relationship between logarithms and exponents is:
[tex]\[
\log_b(a) = c \iff b^c = a
\][/tex]
3. Applying this principle to our equation [tex]\(\log_8(x) = 1\)[/tex], we interpret it as:
[tex]\[
8^1 = x
\][/tex]
4. Simplifying the right side of the equation, we get:
[tex]\[
8^1 = 8
\][/tex]
5. Therefore, the value of [tex]\(x\)[/tex] is:
[tex]\[
x = 8
\][/tex]
So, [tex]\(x = 8\)[/tex].
