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

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

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

simplify

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

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

Solution steps

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

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

lo g_{10} (\frac{x}{y ^{5} z ^{9}})

lo g_{10} (\frac{x ^{2} + y ^{2}}{1000000})

lo g_{7} (\frac{343 b ^{7} y ^{2} - 4}{y ( x + 4 ) ^{2}})

2 lo g_{e} (4) + 2 lo g_{e} (5)

10 lo g_{10} (x) + \frac{2}{3} lo g_{10} (64)

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