Maths

Exponential functions
  • f(x) = b^x where b is base, x is exponent
  • f(x) = e^x - special exponential function where e is 2.7
  • when b>1, the graph passes thru (0,1)
    • bigger the base, the faster it grows
  • when 0<b<1, the graph passes thru (0,1) in decreasing/decent shape
Logarithmic funcitons
  • inverse of b^x is logx with base b
  • Fact: y=logx with base b <=> b^y = x
    • eg: log8 = 3
    • 81 = 3^4 => 4=log81
Write logarithms in Exponential form
  • log8 base 2 = 3 => 2^3=8
  • logp base w = 5 => w^5 = p
Write Exponents in log form
  • 4^2 = 16  => 2 = log16  base 4
  • w=p^k  => k=logw base p

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