### Home > PC > Chapter 8 > Lesson 8.1.3 > Problem8-44

8-44.

Let $k(x) = \frac { 2 ^ { x } } { x ^ { 5 } }$ and $m\left(x\right) = \log\left(k\left(x\right)\right)$

1. Find $m\left(x\right)$ by substituting and using the properties of logarithms to simplify the expression.

$m(x)=\text{log}\left( \frac{2^x}{x^5} \right)$

$=\text{log}(2^x)-\text{log}(x^5)$

$=x\text{log}(2)-5\text{log}(x)$

$\approx0.301x-5\text{log}x$

2. Find $\lim\limits _ { x \rightarrow \infty } k ( x )$ and $\lim\limits _ { x \rightarrow \infty } m ( x )$.

For $k\left(x\right)$, he dominant term is in the numerator.

3. Check your results by graphing or by using the [TABLE] command on your calculator, whichever you prefer.

Use the eTool below to solve this problem.
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