Question

Answer the question it is given in file

Answer 1

Step-by-step explanation:

We have,

$5. {4}^{x + 1} - {16}^{x} = 64$

$\implies \: 5. {4}^{x}.4- {4}^{2x} = 64$

$\implies \: 20.{4}^{x}- ( {4}^{x})^{2} = 64$

$\implies \: ( {4}^{x})^{2} - 20. {4}^{x} + 64 = 0$

$\implies \: ( {4}^{x})^{2} - 16. {4}^{x} - 4. {4}^{x} + 64 = 0$

$\implies \: {4}^{x} \{ {4}^{x}- 16 \} - 4 \{ {4}^{x} + 16 \} = 0$

$\implies \: \{ {4}^{x} - 4 \}\{ {4}^{x}- 16 \} = 0$

$\implies {4}^{x} - 4 = 0 \: \: \: or \: \: \: {4}^{x}- 16 = 0$

$\implies {4}^{x} = 4 \: \: \: or \: \: \: {4}^{x} = 16$

$\implies x = 1 \: \: \: or \: \: \: x = 2$