Question

find the value of x​

Answer 1

Answer:

x= 3/2

Step-by-step explanation:

4^x-3^(x-1/2) = 3^(x+1/2) - 2^(2x-1)

=> 4^(x-1/2+1/2) - 3^(x-1/2) = 3^(x-1/2+1 ) - 4^(x-1/2)

let x-1/2 = k

=> 2× 4^k - 3^k = 3×3^k - 4^k

=> 2×4^k + 4^k = 3×3^k+3^k

=> 4^k(2+1) = 3^k( 3+1)

=> 3×4^k = 4×3^k

=> 4^(k-1) = 3^(k-1)

=> k-1 = 0

=> k = 1

=> x-1/2 = 1

=> x = 1+1/2

=> x = 3/2

hope this helps you