Calculus Examples

$lim_{x \to \infty} \log (5^{\frac{1}{x}})$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\log (lim_{x \to \infty} 5^{\frac{1}{x}})$

Step 1.2

Move the limit into the exponent.

$\log (5^{lim_{x \to \infty} \frac{1}{x}})$

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x}$ approaches $0$ .

$\log (5^{0})$

Step 3

Simplify the answer.

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Step 3.1

Anything raised to $0$ is $1$ .

$\log (1)$

Step 3.2

Logarithm base $10$ of $1$ is $0$ .

$0$