Question

Find x plz help with steps and laws

Answer 1

Answer:

x = 6

Step-by-step explanation:

8² × 4³

---------- = 2^x

  2^x

Cross multiplying,

8² × 4³ = (2^x) × (2^x)

8² × 4³ = 2^(x+x)

8² × 4³ = 2^(2x)

Now,

8² can be written as:

8² = (4 × 2)² = (2² × 2)² = (2³)² = 2^6

And,

4³ can be written as:

4³ = (2²)³ = 2^6

Hence,

            8² × 4³ = 2^(2x)

⇒ 2^(6) × 2^(6) = 2^(2x)

Same base ⇒ We can add powers

∴ 2^(6 + 6) = 2^(2x)

       2^(12) = 2^(2x)

As the bases are equal, we can equate.

     12 = 2x

12 ÷ 2 = x

   ∴  x = 6