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Assymtotic Analysis (Math Tips (Log (Log Properties (\(log(a^b) =…

- - - - If a log has a base or an exponent it becomes canceled out
        
        \(log(n)^7 = 7log(n) \approx log(n)\)
        
        \(log_{10}(N) = \frac{log_2n}{log_{10}n}\)
        The denominator is really a constant
    - - \(log(a^b) = b*log(a)\)
      - \(log(ab) = log(a) + log(b)\)
    - - \(log_{ln(5)}((log n)^{100})\)
        
        \(log((log n)^{100})\)
        
        \(100log((log n))\)
        
        \(log((log n))\)
        
        Same as \(log((x)^{100})\)
        Where x = logn
      - \(log_{ln(5)}((log n^{100}))\)
        
        \(log(100(log n))\)
        
        \(log(100) + (log (log n)))\)
        
        \((log (log n))\)
        Since log(100) is just a constant