What is log_{2}(n^2*log_{2}(n)) ?

The solution to log_{2}(n^2*log_{2}(n)) is 2log_{2}(n)+log_{2}(log_{2}(n))

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simplify log_{2}(n^2*log_{2}(n))

simplify

lo g_{2} (n^{2} \cdot lo g_{2} (n))

2 lo g_{2} (n) + lo g_{2} (lo g_{2} (n))

Solution steps

lo g_{2} (n^{2} lo g_{2} (n))

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (n^{2} lo g_{2} (n)) = lo g_{2} (n^{2}) + lo g_{2} (lo g_{2} (n))

= lo g_{2} (n^{2}) + lo g_{2} (lo g_{2} (n))

Simplify

lo g_{2} (n^{2}) : 2 lo g_{2} (n)

= 2 lo g_{2} (n) + lo g_{2} (lo g_{2} (n))

lo g_{10} (\frac{1}{3}) + lo g_{10} (2)

- lo g_{10} (1.21 \cdot 1 0^{- 3})

ln ∣ 1 ∣ - \frac{3}{2} ln ∣ 5 ∣ + 2 ln ∣ 6 ∣ + C

ln (x^{9} 5 - x)

lo g_{10} (\frac{8 m}{n})

What is log_{2}(n^2*log_{2}(n)) ?
The solution to log_{2}(n^2*log_{2}(n)) is 2log_{2}(n)+log_{2}(log_{2}(n))