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Step-by-step Solution

Evaluate the limit of $x^{2\log \left(x\right)}$ as $x$ approaches $∞$

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Step-by-step explanation

Problem to solve:

$\lim_{x\to∞}\left(\frac{x^{2\log\left(x\right)}}{\left(x\cdot \log\left(x\right)\right)^3}\right)$

Learn how to solve limits by direct substitution problems step by step online.

$\lim_{x\to∞}\left(\frac{x^{2\log \left(x\right)}}{x^3\log \left(x\right)^3}\right)$

Unlock this full step-by-step solution!

Learn how to solve limits by direct substitution problems step by step online. Evaluate the limit of x^(2log(10)) as x approaches ∞. The power of a product is equal to the product of it's factors raised to the same power. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=2 and b=10. Evaluate the limit by replacing all occurrences of x by ∞.

Answer

$\frac{∞^{\log \left(∞^2\right)}}{∞^3\log \left(∞\right)^3}$

Problem Analysis

$\lim_{x\to∞}\left(\frac{x^{2\log\left(x\right)}}{\left(x\cdot \log\left(x\right)\right)^3}\right)$

Time to solve it:

~ 0.09 seconds