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Properties of logarithms Calculator

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1

Solved example of Properties of logarithms

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

Calculating the natural logarithm of $2$

$\lim_{x\to∞}\left(\frac{x^{\frac{4}{\sqrt{3}}10nx}}{\left(10nx\ln\left(x\right)\right)^3}\right)$
3

The power of a product is equal to the product of it's factors raised to the same power

$\lim_{x\to∞}\left(\frac{x^{\sqrt{48}nx}}{1000\ln\left(x\right)^3n^3x^3}\right)$
4

Evaluating the limit when $x$ tends to $∞$

$\frac{∞^{\sqrt{48}n∞}}{1000\ln\left(∞\right)^3n^3∞^3}$
5

Simplifying

$\frac{∞^{\sqrt{48}n∞}}{1000\ln\left(∞\right)^3n^3∞^3}$