EPONENTIALS B1

 

If 5^2m (400^m) = 100,000,000 ; Find m.

Solution

5^2m (400^m) = 100,000,000

(5²)^m (400^m) = 10⁸  [Converting the RHS in exponential form]

(25)^m (400^m) = 10⁸

(25 x 400)^m = 10⁸  [LHS: m is common, so we factor it out]

(10000)^m = 10⁸

(10⁴)^m = 10⁸

10^4m = 10⁸   (Bases are alike, so they cancel out)

4m = 8

4m = 8²

4       4

 

Hence; m = 2

 

TRY THIS…………………………….

 

If 4^2W (4^W) = 128 ; Find W.