Find the values of x in each of the following:

(i) 2^5x÷ 2^x =

(ii) (2³)⁴ = (2²)^x

(iii)

(iv) 5^x-2 × 3^2x-3 = 135

(v) 2^x-5 × 5^x-4 = 5

(vi) 2^x-7 × 5^x-4 = 1250

(i) we have,

2^5x÷ 2^x =

2^5x/2^x = 2^20/5

2^5x-x = 2⁴

4x = 4

x=1

(ii) We have,

(2³)⁴ = (2²)^x

2^3.4 = 2^2.x

12 = 2x

X=6

(iii) We have,

5^2x-x/ 3^2x-x = ()³

5^x/3^x = ()³

()^x = ()³

x=3

(iv) We have,

5^x-2 × 3^2x-3 = 135

5^x-2 × 3^2x-3 = 5

5^x-2 × 3^2x-3 = 5¹³

x-2 =1 ; 2x-3 =3

x=3 ; x= 3

(v) We have,

2^x-5 × 5^x-4 = 5

2^x-5 × 5^x-4 = 5¹ × 2⁰

x-5=0 ; x-4 = 1

x= 4 ; x=1 +4 =5

(vi) We have,

2^x-7 × 5^x-4 = 1250

2^x-7 × 5^x-4 = 2¹ × 5⁴

x – 7=1; x-4 = 4

x= 8; x= 4+4 = 8