Question

Solve this equation
$2 {}^{4x} \times 4 {}^{2} = 32 {}^{x}$
I will mark you brainliest ​

Answer 1

Given:

${\sf{2^{4x} \times 4^2 = 32^x}}$

What To Find:

We have to solve and find the value of x.

How To Find:

To solve this equation we will,

• Make the bases same in both sides.
• Like a linear equation we can solve the exponents.

Solution:

• Making the same bases.

$\sf{2^{4x} \times 4^2 = 32^x}}$

4 can also be written as 2²,

⇒ ${\sf{2^{4x} \times 2^{2 \times 2} = 32^x}}$

32 can also be written as 2⁵,

⇒ ${\sf{2^{4x} \times 2^{2 \times 2} = 2^{5 \times x}}$

Now the bases are same.

• Solving the exponets.

Since the bases are same we won't include them in our equation,

⇒ 4x + 2 × 2 = 5x

Multiply 2 by 2,

⇒ 4x + 4 = 5x

Take 4x to RHS,

⇒ 4 = 5x - 4x

Subtract 4x from 5x,

⇒ 4 = x

∴ Thus, the value of x is 4.