Question

log in baza 3 din 9 supra radical din 3

Answer 1

$\log_{3}\left( \frac{9}{ \sqrt{3} } \right) = \log_{3}\left( \frac{9 \sqrt{3} }{3} \right) = \log_{3}(3 \sqrt{3} ) \\ \implies 3 {}^{x} = 3 \sqrt{3} \implies 3 {}^{x} = 3\cdot3 {}^{ \frac{1}{2} } \\ 3 {}^{x} = 3 {}^{ \frac{2 + 1}{2} } \implies3 {}^{x} = 3 {}^{ \frac{3}{2} } \iff \bold{\: x = \frac{3}{2} }$