EXPONENTIALS 4

Find x if 64^x = 0.125; find x.

Solution

64^x = 0.125

(2⁶)^x = 0.125          [since 64=2⁶ ]

2^6x = 0.125          

2^6x = ¹²⁵/₁₀₀₀     [converting 0.125 into fraction]       

2^6x = ¹/₈    [after simplifying]       

2^6x = 8^-1           [since ¹/_a=a^-1]

2^6x = (2³)^-1

2^6x = 2^{3 x-1}           

2^6x = 2^-3           [since (a^c)^d =a^cd]

2^6x = 2^-3           [same bases cancel out]

6x = -3         

6x = -3 ^-1        

6      6 ₂

x= ^-1/2

Hence x= ^-1/2  .

TRY THIS…………………….

Find x if 16^2m = 0. 5; find m.