EXPONENTIALS 1

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

Solution

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

(5²)^w (400^w) = 100,000

(25)^w (400^w) = 100,000

(25 x 400)^w = 100,000

(10000)^w = 100,000

(10⁴)^w = 10⁵   [since 10⁵ = 100,000]

10^4w = 10⁵   (Bases are alike, so they cancel out)

4w = 5

4w = 5

4       4

w = ⁵/4

TRY THIS…………………………….

NECTA 2004 QN. 4b

If 3^2t (4^t) = 6 ; Find t.