Exponential Equations(2)

Example 1:

Solve each equation:

a)  (3) ^x = 1/9                         

    

     (3) ^x = (3)^{- 2}                           

        X = - 2 

b)  (5) ^x = 1/125

     (5) ^x = (5)^- 3

        X = - 3

c)  (2) ^{x + 1} = 1/16

     (2) ^{x + 1} = (2)^{- 4}

      X + 1 = - 4

       X = - 4 - 1

        X = - 5

d)   (3) ^{x - 2} = 1/9

       (3) ^{x - 2} = (3)^{- 2}

       X – 2 = -2

       X = - 2 + 2

        X = 0

Example 2:

Solve each equation:

a)  (8)^x = 1/ 64                         

    

     (8)^x = ( 8)^{- 2}                           

        X = - 2 

b)  (3)^x = 1/81

     ( 3)^x = ( 3)^{- 4} 

        X =  - 4

c)  (5)^x+1 = 1/125

     (5)^x+1 = (5)^{- 3}

      X + 1 = - 3

       X =- 3 - 1

        X = - 4

d)   (3) ^{x - 3} = 1/9

       (3) ^{x - 3} = (3)^{- 2}

       X – 3 = - 2

       X = - 2 + 3

        X = 1

Example 3:

Solve each equation:

a)  (5)^x = 1/625                 625 = 5 ×5×5×5                    

    

     (5)^x = (5) ^{- …..}                           

        X = -  .. 

b)  (2)^x = 1/2                          

     ( 2)^x = (2)^-1 

        X = …..

c)  (3)^x+2 = 1/ 81

     (3)^x+2 = (3)^-....

      X + 2 = - .. .

       X = - ... - 2

        X = - ......

d)   (4)^{x - 3} = 1/16

       (4)^{x - 3} = (4)^....

       X – 3 = ....

       X = .......

Example 4:

Solve each equation:

a)  (2/5) ^x = 25/4                         

    

     (2/5) ^x = (5/2)²

    (2/5) ^x = (2/5)^{- 2}

   

        X = - 2 

b)  (2/3) ^x = 8/27

     (2/3) ^x = (2/3)^{- 3}

        X = - 3

c)  (2/5) ^{x + 1} = 125/8

     (2/5) ^{x + 1} = (2/5)^{- 3}

      X + 1 = - 3

       X =- 3 - 1

        X = - 4

d)   (2/7) ^{x - 3} = 343/8

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

       X – 3 =  - …..

       X = -  …. + 3

        X = 0