EXPONENTIAL and LOGARITHMIC FUNCTIONS

    Some common Exponential and Logarithmic relationships include the following:
  • x = logb y or y = bx; where b = base (2 = log10 100; 100 = 102)

  • y = logb x or x = by

  • y = ln x (x = ey) or x = ln y (y = ex)

  • logb 1 = 0
  • logb b = 1

  • y = ex and y = e-x

  • logb br = r

  • blogbm = m

    • 10log m = m and eln m = m

  • bm = bn; m = n

  • logb mr = r(logbm)

  • logb(m/n) = logbm - logbn
  • logb(mn) = logbm + logbn

EXPONENTIAL and LOGARITHMIC EQUATIONS

  • y = logb x or x = by; where b = base
  • x = logb y or y = bx; where b = base
  • eln x2 = x2

  • 10log x2 = 25; x2 = 25; x = 5, and -5

  • log2 x = 4; 2y = x; 24 = x; x = 16

  • 25x+2 = 53x-4; (52)x+2 = 53x-4; 52x+4 = 53x-4; 2x+4 = 3x-4; x = 8

  • 5 + 4x-1 = 12; 4x-1 = 7;
    ln4x-1 = ln7; x-1(ln4) = ln7;
    x-1 = ln7/ln4;
    x = ln(7/4) + 1; x = (ln7 - ln4) + 1

  • ln(x+1) = 7; ey = x+1
    e7 = x+1; x = e7 - 1

  • Gereral Radioactive Decay:
    No/n = Noe-kt
    No/n / No = e-kt; 1/n = e-kt
    n = ekt; ln(n) = kt; t = ln(n)/k

      Where:
    • No = initial amount
    • n = 1.....100
    • k = decay constant
    • t = time

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