If, $2^{x+y-2z}=8^{8z-5-y};5^{4y-6z}=25^{y+z};3^{4x-3z}=9^{x+z}$ then the value of $2x + 3y +5z$ is :

44

$2^{x+y-2z}=8^{8z-5-y};5^{4y-6z}=25^{y+z};3^{4x-3z}=9^{x+z}$ then the value of $2x + 3y +5z$

We know that,

a^p × a^q = a^{{p + q}}

2^x+y-2z = 8^8z-5-y

= 2^x+y-2z = 2^3(8z-5-y)

Comparing on power

= x + y - 2z = 24z - 15 - 3y

= x + 4y - 26z = -15     ----(A)

5^4y-6z = 25^y+z

= 5^{4y - 6z} = 5^{2 (y + z)}

Comparing on power

= 4y - 6z = 2 (y + z)

= 4y - 6z = 2y + 2z

= 2y = 8z

= y = 4z     ----(B)

3^4x-3z = 9^x+z

= 3^4x-3z = 3^{2(x + z)}

Comparing on power

= 4x - 3z = 2x + 2z

= 4x - 2x = 2z + 3z

= 2x = 5z

= x = 2.5z     ----(C)

From equation (A), equation (B) and equation (C)

= x + 4y - 26z = -15

= 2.5z + 4 (4z) - 26z = - 15

= 2.5z + 16z - 26z = - 15

= - 7.5z = - 15

= z = 2

From equation (B)

y = 4 × 2

= y = 8

From equation (C)

x = 2.5 × 2

= x = 5

Now, 

2x + 3y + 5z

= 2 × 5 + 3 × 8 + 5 × 2

= 10 + 24 + 10 = 44