EXPONENTIAL EQUATIONS 1

Find x if 64^x = 0.25; find x.

Solution

64^x = 0.25

(2⁶)^x = 0.25          [since 64=2⁶ ]

2^6x = 0.25          

2^6x = ²⁵/₁₀₀     [converting 0.25 into fraction]       

2^6x = ¹/₄    

2^6x = 4¹           [since ¹/_a=a^-1]

2^6x = (2⁴)¹

2^6x = 2^4x1           

2^6x = 2⁴           [since (a^c)^d =a^cd]

2^6x = 2⁴           [same bases cancel out]

6x = 4         

6x = 4 ²        

6      6 ₃

x= ²/3

Hence x= ²/3

TRY THIS…………………….

Find x if 16^x = 0.125; find x.