Assymtotic Analysis
Math Tips
Log
Log Tricks
If a log has a base or an exponent it becomes canceled out
log(n)7=7log(n)≈log(n)
\(log_{10}(N) = \frac{log_2n}{log_{10}n}\)
The denominator is really a constant
Log Properties
\(log(a^b) = b*log(a)\)
Good Problems
\(log_{ln(5)}((log n)^{100})\)
\(log((log n)^{100})\)
\(100log((log n))\)
\(log((log n))\)
\(log_{ln(5)}((log n^{100}))\)
Same as \(log((x)^{100})\)
Where x = logn
\(log(100(log n))\)
\(log(100) + (log (log n)))\)
\((log (log n))\)
Since log(100) is just a constant
\(log(ab) = log(a) + log(b)\)