Exponential Equations(4)

Example 1:

Solve each equation:

a)  (3) ^x = (5) ^x                            

     (3) ⁰ = (5)⁰ = 1                              

        X = 0 

b)  (5) ^{x- 1} = (7) ^{x- 1}   

     (5) ⁰ = (7)⁰ = 1

        X - 1 = 0

        X= 0 + 1 = 1 

c)  (2) ^{x + 1} = (3) ^{x + 1}   

     (2)0 = (3)⁰ =1

      X + 1 = 0

       X = 0 - 1

        X = - 1

d)   (3) ^{x - 2} = (11) ^{x - 2}    

       (3) ⁰ = (11)⁰ = 1

       X – 2 = 0

       X = 0 + 2

        X = 2

Example 2:

Solve each equation:

a)  (9)^x = (6)^x                            

    

     (9)⁰ = ( 6)⁰ 1

        X = 0 

b)  (2)^x = (7)^x

     ( 2)⁰ = ( 7)⁰

        X =  0

c)  (5)^x+1 = (4)^x+1   

     (5)⁰ = (4)⁰

      X + 1 = 0

       X =0 - 1

        X = - 1

d)   (2) ^{x - 3} = (7) ^{x - 3}   

       (2) ⁰ = (7)⁰

       X – 3 = 0

       X = 0 + 3

        X = 3

Example 3:

Solve each equation:

a)  (17)^x =  (19)^x                                                

    

     (17)^.. = (19)   ^….=1^.                           

        X =    .. 

b)  (2)^x = ( 7)^x                            

     ( 2)^… = (7)^…. =1  

        X = …..

c)  (3)^x+2 = (5)^x+2 

     (3)⁰ = (5) ^....= 1

      X + 2 =   .. .

       X =   ... - 2

        X = - ......

d)   (2)^{x - 3} = (13)^{x - 3}

       (2)^… = (13)^.... = 1

       X – 3 = ....

       X = .......

Example 4:

Solve each equation:

a)  (2/5) ^x =  (3/7) ^x                         

    (2/5) ⁰ = (3/7)⁰ =1

   

        X = 0 

b)  (2/3) ^x = (1/5) ^x

     (2/3) ⁰ = (1/5)⁰ =1

        X = …..

c)  (2/5) ^{x + 1} =  (3/11) ^{x+ 1}

     (2/5)^….. = (3/11)^….. =1  

      X + 1 = …..

       X =…. - 1

        X = - ….

d)   (1/7) ^{x - 3} =  (3/4) ^{x - 3}

       (1/7) ⁰ = (3/4) ^….  = 1           

       X – 3 =    …..

       X =    …. + 3

        X = ……