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How to Find the Logarithm of a Number

According to Purplemath, exponentials and logarithms are opposites. Recall that an exponential function is one in which a base number is raised to an exponential power, e.g., b^y=x. If the base number b is greater than zero and not equal to one than it can be re-expressed as a logarithm. By definition, the exponential expression b^y = x can be re-expressed as log_b x = y if b > 0 and b is not equal to 1.

Things You'll Need

Scientific Calculator

Instructions

- 1
  Write both the exponential equation and its equivalent logarithm.
  
  b^y=x and log_b x = y
- 2
  Simplify the exponential equation and see if that reveals the solution for y.
- 3
  Simplify the logarithm by applying one or more of the basic properties of logarithms:
  
  (a) log_b 1 = 0
  
  (b) log_b b = 1
  
  (c) log_b uv = log_b u + log_b v
  
  (d) log_b (u/v) = log_b u -- log_b v
  
  (e) log_b u^r = r log_b u
- 4
  Repeat the above steps until you have a solution.
- 5
  Use your scientific calculator as appropriate when solving the logarithm. For example, using a TI-89 Titanium you enter in the equation LOG(x, b) to solve log_b x.

Numerology