EXPONENTIALS K4

 

Find x if 128^x = 0.125; find x.

 

Solution

 

128^x = 0.125

 

(2⁷)^x = 0.125          [since 128=2⁷ ]

 

2^7x = 0.125      

    

2^7x = ¹²⁵/₁₀₀₀       [converting 0.125 into fraction]  

     

2^7x = ¹/₈             [after simplifying]

      

2^7x = 8^-1             [since ¹/_a=a^-1]

 

2^7x = (2³)^-1

 

2^7x = 2^{3 x-1}   

        

2^7x = 2^-3            [since (a^c)^d =a^cd]

 

2^7x = 2^-3            [same bases cancel out]

 

7x = -3         

 

7x = -3

7       7

 

x= ^-3/7

 

Hence x= ^-3/7  .

 

TRY THIS…………………….

 

 

Find x if 64^4m = 0. 5; find m.