• 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