Logarithm Basics

  • logarithms represent the exponent that the base must be raised to be equal to the argument
  • (in these lessons I'll write log base b of c as "log[b]c"
  • so, if log[b]c = a, then b^a = c
    • base^logarithm = argument


Common Guidelines for Logarithms

  • in log[b]c = a,
    • if c = 1, then log[b]c = 0
      • because b^a = c, b^a = 1, "a" must be 0 because you must raise "b" to the zeroth power to get 1
    • if b = c, then log[b]c = 1
      • because b^a = c, b^a = b, "a" must be 1 (2^1 = 2, 3^1 = 3, etc)


Writing Exponential Expressions as a Logarithm


Writing Logarithms as an Exponential Expression


Argument Raised to the Exponent

  • log[b](b^n) = n
    • because if log[b]c = a, then b^a = c
    • sub in "b^n" for c, and "n" for a
    • the result is b^n = b^n, where both sides are equal


Evaluating Logarithms

  • if possible, write the argument as a power (b^n) with the same base as the base of the logarithm (b)


Estimating Logarithms

Complete and Continue