Calculus Examples

$lim_{x \to e^{2}} \frac{\log (x)}{\log (e)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{1}{\log (e)}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{\log (e)} lim_{x \to e^{2}} \log (x)$

Step 1.2

Move the limit inside the logarithm.

$\frac{1}{\log (e)} \log (lim_{x \to e^{2}} x)$

Step 2

Evaluate the limit of $x$ by plugging in $e^{2}$ for $x$ .

$\frac{1}{\log (e)} \log (e^{2})$

Step 3

Simplify the answer.

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Step 3.1

Combine $\frac{1}{\log (e)}$ and $\log (e^{2})$ .

$\frac{\log (e^{2})}{\log (e)}$

Step 3.2

Expand $\log (e^{2})$ by moving $2$ outside the logarithm.

$\frac{2 \log (e)}{\log (e)}$

Step 3.3

Cancel the common factor of $\log (e)$ .

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Step 3.3.1

Cancel the common factor.

$\frac{2 \log (e)}{\log (e)}$

Step 3.3.2

Divide $2$ by $1$ .

$2$