Question

If
$\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } } = {7}^{x}$
then find the value of x.
Answer is 31/32, kindly provide explanation.​

Answer 1

$\huge\color{cyan}\boxed{\colorbox{black}{ANSWER ❤}}$

$\red{\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } } }= \purple{{7}^{x}}$

$\red{ {7}^{ \frac{1}{2} } \times {7}^{ \frac{1}{2} } \times {7}^{ \frac{1}{2} } \times {7}^{ \frac{1}{2} } \times {7}^{ \frac{1}{2} } } = \purple{ {7}^{x} }$

$\red{ {7}^{ \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} } } = \purple{ {7}^{x} }$

$\red{ {7}^{ \frac{5}{2} } } = \purple{ {7}^{x} }$

$\purple{x} = \red{ \frac{5}{2} }$