Question

Calculati 49^1\2log in baza 7 din 1\4 (49 la puterea unu supra doi logaritm in baza 7 din 1 supra patru ).

Answer 1

$49^{\dfrac{1}{2}\log_\big 7 \dfrac{1}{4}} = \\ \\ =49^{\dfrac{1}{2}\cdot \log_\big 7 \dfrac{1}{4}}= \\ \\ = \left(49^{\dfrac{1}{2}}\right)}^{\log_\big 7 \dfrac{1}{4}} = \\ \\ = \sqrt{49}^{\log_\big 7 \dfrac{1}{4}} = \\ \\ = 7^{\log_\big 7 \dfrac{1}{4}} = \\ \\ = \dfrac{1}{4}$