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Solving-Exponential-and-Logarithmic-Equations

Page history last edited by Kristen Fouss 11 years, 7 months ago

  LOGARITHMIC AND EXPONENTIAL                                           EQUATIONS                                                                                     

     THERE ARE 3 MAIN TYPES OF EQUATIONS

     1.  eq=a^x=b

          a. First you want to get the same base on both sides

               ex. Solve .  

                         eq=6^x=7776               Get the same base on both sides                

                         eq=6^x=eq=6^5                   Put the exponents equal to each other

                         x=5

          b. OR you can take the log of both sides

               ex. Solve.

                         eq=6^x=7776               Take the log of both sides

                         logeq=6^x=log7776      Move the exponents out in front of the log        

                         xlog6=log7776       Divide to get the x by itself

 

                         x=eq=\frac{log7776}{log6}

                         x=5

     2.eq=log_xa=b

          a. To solve this type of equation go to exponential form ( eq=x^b=a )

               ex. Solve.

                    eq=log_x343=3                  

                    eq=x^3=343                 Change the equation to exponential form. (eq=x^b=a

                    eq=\sqrt[3]{x^3 }=\sqrt[3]{343}          Take the cube root of both sides

                    eq=x=7

 

     3. eq=log_xa=log_xb

          a.To solve this type of equation you can remove the logs from each side of the equation. You can only do this if the logs have the same base.

               So if the logs have the same base, then a=b.

                    ex. Solve.

                         eq=log_5x=log_510           Since both the bases are the same put x equal to 10    

                         eq=x=10

 

Solve the following type of equations by using the best method:

 

               1.  eq=2^x=8

                    eq=log2^x=log8

                    eq=xlog2=log8

                    eq=x=\frac{log8}{log2}

                    eq=x=3

 

               2. eq=log_9x=2                                                   

                         eq=x=9^2

                         eq=x=81                                             

 

               3. eq=5^x=25

                    eq=5^x=5^2

                    eq=x=2

 

 

                                                                                                                                             

 

For More Help watch this instructional video.

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http://www.youtube.com/watch?v=pP3NunYYhzk

also visit his website at www.justmathtutoring.com

 

CHECK OUT THESE WEBSITES FOR MORE HELP!!!!!!

www.yaymath.org

www.justmathtutoring.com

 

http://www.regentsprep.org/Regents/math/algtrig/ATE9/logEquationPrac.htm

 

 

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