# How do you write the exponential notation for log_8 1 = x?

${8}^{x} = 1$
For any positive number $b \ne 1$, ${\log}_{b} \left(x\right)$ and ${b}^{x}$ are inverse functions of one another.
So given ${\log}_{8} \left(1\right) = x$ apply exponentiation using $8$ on both sides to find:
${8}^{x} = {8}^{{\log}_{8} \left(1\right)} = 1$