Question

b) 1. Să se calculeze: (log3 4 - log3 4/9) • log5 3√5​
dau coroană!!!

Answer 1

Salutare ! (っ◔◡◔)っ

Răspuns:

$( log_{3}(4) - log_{3}( \frac{4}{9} ) ) \times log_{5}(3 \sqrt{5} ) = ( log_{3}(4) - ( log_{3}(4) - log_{3}(3 {}^{2} ) )) \times ( log_{5}(3) + log_{5}(5 {}^{ \frac{1}{2} } ) ) = ( log_{ 3}(4) - ( log_{3}(4) - 2)) \times ( log_{5}(3) + \frac{1}{2} ) = ( log_{3}(4) - log_{ 3}(4) + 2) \times ( log_{5}(3) + \frac{1}{2} ) = 2( log_{5}(3) + \frac{1}{2} ) = 2 log_{5}(3) + \frac{1}{2}$

Explicație pas cu pas:

$formule \: \: \: folosite \: \: log_{a}( \frac{x}{y} ) = log_{a}(x) - log_{a}(y)$

$log_{a}(x \times y) = log_{a}(x) + log_{a}(y)$

$log_{a}(a {}^{x} ) = x$

《 Sa ai o zi frumoasa ! 》