Math equations and formulas
Logarithms
The fundamental property of a logarithm (base b) is:
$$\displaystyle y = b^x \iff x = log_b y \iff b = \sqrt[x ] y \qquad \small{for} b \gt 1, y \gt 0
Properties:
log2 xy=logx+logylog2 x/y=logx−logylog2 xy=y log xlog2 1=0log2 2=1 Summations
i=1∑n i=2n(n+1)i=1∑n i2=62n3+3n2+ni=0∑n 2i=2n+1−1i=0∑n ai=a−1an+1−1i=1∑n i2i=(n−1)2n+1+2i=1∑n ⌈log2 (i+1)⌉=(n+1) log2 (n+1)−ni=1∑n ⌊log2 i⌋=(n+1) log2 (n+1)−2n