Solve the Reciprocal Expression: 1/ln8 Step-by-Step

To solve the problem, follow these steps:

• Step 1: Identify the expression to simplify, $\frac{1}{\ln 8}$.
• Step 2: Apply the change of base formula:

Using the change of base formula, we have:
$\log_8 e = \frac{\ln e}{\ln 8}$ Since $\ln e = 1$, substituting gives:
$\log_8 e = \frac{1}{\ln 8}$

Therefore, the expression $\frac{1}{\ln 8}$ can be rewritten as $\log_8 e$.

Thus, the correct choice is $\log_8 e$.