Solving Logarithmic Equations 2 - Cool Math

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Algebra Exponentials and Logarithms Solving Log Equations previouscontinue1234567of 7 Solving Log Equations

OK, ready to go!  Let's start by doing some that are already in the nice forms:

Log to the base 2( 4x ) = 3We can't solve anything with thisobnoxious Log in here -- he's blockingthe x!  So...  We need to get rid of him.  And who can do that?His inverse!

So...  Zap both sides with2^x!

2^( Log to the base 2( 4x ) ) = 2^3 ... the 2 and the Log to the base 2 cancel out ... 4x = 8 ... Now, it's easy! ... x = 2

With that inverse trick, these are really pretty simple.

Let's do some more:

Solve Log( 50x ) = 3Remember that this is really

Log to the base 10( 50x ) = 3

Hit it with the inverse:

10^( Log( 50x ) ) = 10^3 ... the 10 and the Log cancel out ... 50x = 1000 ... x = 20

 

previouscontinue1234567of 7
  • The Exponential Monster
  • Alien Amoebas
  • Compound Interest
  • Continuous Compounding
  • Annuities
  • Population Growth
  • Graph of Exponentials
  • What's a Logarithm?
  • Some Special Logs
  • Inverse Tricks
  • Solving Exponential Equations
  • Solving for Time and Rates
  • More Ways to Use This Stuff
  • Tricks to Help with Solving Log Equations
  • Solving Log Equations
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