Logarithmic Equations

                    Lesson 1

                                                                                                                                                                         

                                                                                               

                                          Properties:

 

logbm.n=logbm+logbn

 

 

lnab= lna+lnb

logbm/n=logbm-logbn

 

 

lna/b= lna-lnb

logbmr=rlogbm

 

 

lnab=blna

 

                                                            Problem:   Solve for x: 8 + 4lnx = 24       

 

                                                            Solution     Isolate the logarithmic expression first

                                                            Step 1:         4lnx = 24 - 8;                                                                                  

                     

                                                            Solution     4lnx = 16;               

Step 2:                        

                                                                                         

                                                            Solution     ln x = 16/4;

                                                            Step 3:         ln x = 4                   

 

                                                            Solution     Remember that ex and ln x are inverse functions.

                                                            Step 4:         eln x=e4 ;x=e4   (eln x=x)     

 

                                                            Solution     Answer: x=e4

 Step 5:                                                        

 Complete                                                                   

                                                                                                                               

                                                             Try two practice problems:  

 

                                                                                 Solve for x:

 

A.

2 + 2lnx = 14

B.

Log5 (x+1) = 2

 

                                                                                               

 

 

 

 

 

        

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