Question

find the value of X​

Answer 1

Answer:

x=1

Step-by-step explanation:

25^x × 16^(x+1) = 6400

25^x × 16^(x+1) = 64×100

25^x × 4^2(x+1) =4^3 × 25×4

25^x × 4^2(x+1) =4^4×25

Comparing both sides we have,

either x=1 or 2(x+1)=4 i.e. x =1

Answer 2

${25}^{x} \times {16}^{x + 1} = 6400 \\ \\ = > { ({5}^{2} )}^{x} \times { ({2}^{4} )}^{x + 1} = 6400 \\ \\ = > {5}^{2x} \times {2}^{4x + 4} = 2 \times 2 \times 2 \times 2 \times2 \times 2 \times 2 \times 2 \times 5 \times 5 \\ \\ = > {5}^{2x} \times {2}^{4x + 4} = {5}^{2} \times {2}^{8}$

On comparing :

2x = 2 or 4x+4 = 8

=> x = 1 or 4x = 4 => x = 1

So, the value of x will be 1

@ItsChampion ✌️