# Step-by-step Solution

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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.

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

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 ∞.

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

### Problem Analysis

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

### Main topic:

Limits by direct substitution

~ 0.09 seconds