Calculus Examples

$\frac{lim_{x \to 8} \ln (\ln (x^{100}))}{\ln (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\frac{\ln (lim_{x \to 8} \ln (x^{100}))}{\ln (x)}$

Step 1.2

Move the limit inside the logarithm.

$\frac{\ln (\ln (lim_{x \to 8} x^{100}))}{\ln (x)}$

Step 1.3

Move the exponent $100$ from $x^{100}$ outside the limit using the Limits Power Rule.

$\frac{\ln (\ln ({(lim_{x \to 8} x)}^{100}))}{\ln (x)}$

Step 2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{\ln (\ln (8^{100}))}{\ln (x)}$