Question

Find value of x :
1. 2^{x} + 2^{x} + 2^{x} = 192
2. 8^{255} = (32) ^{x}
3. 2^{2x+2} = 4^{2x-1}

Answer 1

1. 2^x+2^x+2^x=192
2^x+2^x+2^x= 2^6+2^6+2^x
Comparing LHS and RHS we get
x=6
3. 2^(2x+2)=2^2×(2x-1)
2x+2=4x-2
2x=4
x=2

Answer 2

Hi friend,
1) let 2ˣ=t then 2ˣ+2ˣ+2ˣ=192 ⇒⇒3t=192⇒t=64 but t=2ˣ=64=2⁶
    as bases are equal equating the powers we get x=6

2)8²⁵⁵=32ˣ
   8 can be written as 2³ and 32 as 2⁵ 
So,
   2³⁽²⁵⁵⁾=2⁵ˣ
Now equating the powers 
 3(255)=5x
 x=255(3)/5
 x=153

3)2²ˣ⁺²=2²⁽²ˣ⁻¹⁾
 equating powers as bases are same
2x+2=4x-2
4=2x
x=2

HOPE THIS HELPS U!!