Exponential Equations(3)

Example 1:

Solve each equation:

a)  (3) ^x = 1                          

    

     (3) ^x = (3)⁰                              

        X = 0 

b)  (5) ^{x- 1} = 1

     (5) ^{x- 1} = (5)⁰  

        X - 1 = 0

        X= 0 + 1 = 1 

c)  (2) ^{x + 1} = 1

     (2) ^{x + 1} = (2)⁰

      X + 1 = 0

       X = 0 - 1

        X = - 1

d)   (3) ^{x - 2} = 1

       (3) ^{x - 2} = (3)⁰

       X – 2 = 0

       X = 0 + 2

        X = 2

Example 2:

Solve each equation:

a)  (8)^x = 1                          

    

     (8)^x = ( 8)⁰

        X = 0 

b)  (3)^x = 1

     ( 3)^x = ( 3)⁰

        X =  0

c)  (5)^x+1 = 1

     (5)^x+1 = (5)⁰

      X + 1 = 0

       X =0 - 1

        X = - 1

d)   (3) ^{x - 3} = 1

       (3) ^{x - 3} = (3)⁰

       X – 3 = 0

       X = 0 + 3

        X = 3

Example 3:

Solve each equation:

a)  (5)^x = 1                                                 

    

     (5)^x = (5)^…..                           

        X =    .. 

b)  (2)^x = 1                           

     ( 2)^x = (2)^….. 

        X = …..

c)  (3)^x+2 = 1

     (3)^x+2 = (3)^....

      X + 2 =   .. .

       X =   ... - 2

        X = - ......

d)   (4)^{x - 3} = 1

       (4)^{x - 3} = (4)^....

       X – 3 = ....

       X = .......

Example 4:

Solve each equation:

a)  (2/5) ^x = 1                         

    (2/5) ^x = (2/5)⁰

   

        X = 0 

b)  (2/3) ^x = 1

     (2/3) ^x = (2/3)⁰

        X = …..

c)  (2/5) ^{x + 1} = 1

     (2/5) ^{x + 1} = (2/5)^…..

      X + 1 = …..

       X =…. - 1

        X = - ….

d)   (2/7) ^{x - 3} = 1

       (2/7) ^{x - 3} = (2/7) ^…..            

       X – 3 =    …..

       X =    …. + 3

        X = ……