Question

use a graph or a table to find the following limit. \\(\lim\limits_{x\to\infty} \log_{6}(x)\\) \\(\lim\limits_{x\to\infty} \log_{6}(x) = \boxed{\infty}\\) (simplify your answer.)

Explanation:

Step1: Recall Logarithm Behavior

For a logarithmic function \( y = \log_b(x) \) where \( b > 1 \), as \( x \) approaches \( \infty \), the function values increase without bound. Here, \( b = 6 > 1 \).

Step2: Apply Limit to \( \log_6(x) \)

As \( x \to \infty \), \( \log_6(x) \) grows indefinitely. So the limit is \( \infty \).

Answer:

\(\infty\)