Question

Să se calculeze $log_{3} (5- \sqrt{7}) + log_{3}(5+ \sqrt{7}) - log_{3}2$.

Answer 1

=log₃ (5-√7)(5+√7)/2 =log₃(25-7)/2 =log₃9 = 2

Answer 2

$\displaystyle \mathtt{log_3 \left(5- \sqrt{7}\right) +log_3\left(5+ \sqrt{7}\right)-log_32=log_3 \frac{\left(5- \sqrt{7}\right)\left(5+ \sqrt{7}\right) }{2} =}\\ \\ \mathtt{=log_3\frac{25-7}{2}=log_3 \frac{18}{2} =log_39=log_33^2=2log_33=2 }$