Question

Find value of x ---​

Answer 1

${2}^{5x} + {2}^{x} = \sqrt[5]{ {2}^{20} }$

As we know when

$\sqrt[x]{a} = a {}^{ \frac{1}{x} }$

So,

${2}^{5x} + {2}^{x} = {2}^{20 \times \frac{1}{5} } \\ \\ {2}^{5x} + {2}^{x} = {2}^{4}$

As we know when

${x}^{a} + {x}^{b} = {x}^{c} \\ \\ a + b = c$

So,

${2}^{5x} + {2}^{x} = {2}^{4} \\ \\ 5x + x = 4 \\ \\ 6x = 4 \\ \\ x = \frac{4}{6} \\ \\ x = \frac{2}{3}$