274xVx 2 1 812x4 32 Solution274x sqrtx812x sqrtx 32sqrtx

Solution

27^(4x - sqrtx)/81^(2x +sqrtx) = 3^(2sqrtx)

3^(12x - 3sqrtx)/3^(8x +4sqrtx) = 3^(2sqrtx)

3^(12x - 3sqrtx -8x - 4sqrtx) = 3^(2sqrtx

Equate the exponenets from both sides:

12x - 3sqrtx -8x - 4sqrtx = 2sqrtx

4x = 9sqrtx

squarte both sides:

16x^2 = 81x

x( 16x - 81) =0

x =0

x = 81/16

Solution : x=0 , 81/16