Question

4^{2x} =256-16^{x} solve.

Answer 1

Answer:

The answer is $x=\frac{7}{4}$

Step-by-step explanation:

Given   $4^{2x}=256-16^x$

      $\Rightarrow ((2)^2)^{2x}=256-(2^4)^x$

     $\Rightarrow (2)^{4x}=256-(2^{4x})$, since $(a^m)^n=a^{mn}$

     $\Rightarrow 2^{4x}+2^{4x}=256\\\Rightarrow 2(2^{4x})=256\\\Rightarrow 2^{4x}=\frac{256}{2}=128\\\Rightarrow 2^{4x}=2^7$

Equate exponent from both sides as base is same

  $\Rightarrow 4x=7\\\Rightarrow x=\frac{7}{4}$