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

\(log(ab) = log(a) + log(b)\)