Algebra 2 Solving Log Equations
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Solving Log Equations

 

 The rules of logs look a bit like the rules of exponents.

 

 

 
 and ... (watch closely)

 Log ab = b Log a

 
 This is the most valuable rule about logs.
 It lets you do an amazing thing ...
 
 Say you had  the equation:

 200 = 2X

 
 What exponent do you raise 2 to, to get 200?
 Or to say it another way ...
 How many 2's do you have to multiply together to get 200?
 (2x2x2x2x ...)
 
 Here's the way to solve this one:
 
 We can do almost anything we want to do to an equation
 as long as we do the same thing to both sides of the equation.
 Right now, we're going to take the log of both sides.
 We can use any log base we like,
 so chose a base that we have a key for on our calculator.
 That probably means using 10 or e.
 

 200 = 2X

 Ln 200 = Ln 2X

 
 Here it is. The reason logs are still taught in math.
 When we have something like the right side of this equation
 we can change it like this:
 

 Ln 2X = X Ln2

 
 That's right. If you have the log of a term with an exponent,
 you can move the exponent to the left of the ln or log.
 That turns the exponent into a plain number factor.
 Ans a number factor is WAY easier to deal with than an exponent!

 

 
 Now back to the problem ...

 

 200 = 2X

 Ln 200 = Ln 2X

 Ln 200 = X Ln 2

 
 Now divide both sides by Ln 2 and cancel ...

 

 
 Ln 2 and Ln 200 are just numbers!
 We can punch them up on a calculator
 and solve for X ...

 

 

   copyright 2005 Bruce Kirkpatrick

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