EXPONENTIALS 1B

If 3^2w (40^w) = 1000000^w-10 ; Find w.

Solution

5^2w (40^w) = 1000000 ^w-10

(5²)^w (40^w) = 10^6(w-10)

(25)^w (40^w) = 10^6w-60

(25 x 40)^w = 10^6w-60

(1000)^w = 10^6w-60

(10³)^w = 10^6w-60

10^3w = 10^6w-60  (Bases are alike, so they cancel out)

3w = 6w-60

0= 6w-3w – 60  [collecting letters together]

0= 3w – 60  [collecting letters together]

60 = 3w

²⁰60= 3w       [dividing by 3 on both sides]

    3     3

w = 20

TRY THIS…………………………….

If 4^2t (4^t) = 128^t+5 ; Find t.