EXPONENTIALS 8

If 5^2w (4^w) = 0.00001 ; Find w.

Solution

5^2w (4^w) = 0.00001

(5²)^w (4^w) = 0.00001

(25)^w (4^w) = 0.00001

(25 x 4)^w = 0.00001

(100)^w = 0.00001

(10²)^w = 10^-5 (Since  0.00001=10^-5)

10^2w = 10^-5   (Bases are alike, so they cancel out)

2w = -5

2w = -5

2       2

Hence w = ^-5/2 answer.

TRY THIS…………………………….

If 3^2t (4^t) = 256 ; Find t.