Question

\[\sqrt[x]{8}=2\]

Answer 1

\[\LARGE \sqrt[x]{8}=2\]


\[\LARGE 8^{\frac{1}{x}}=2\]


\[\LARGE (2^3)^{\frac{1}{x}}=2\]


\[\LARGE 2^{\frac{3}{x}}=2\]


\[\LARGE 2^{\frac{3}{x}}=2^1\]


Since the bases are equal, the exponents are equal

\[\LARGE \frac{3}{x}=1\]


\[\LARGE 3=1*x\]


\[\LARGE 3=x\]


\[\LARGE x=3\]


So the answer is \[\LARGE x=3\]