Question

Cat este log 2 la 10-log 2 la 5+3 la 1-log 3 la4

Answer 1

$log_{2}10-log_{2}5+3^{1-log_{3}4}=\\\\log_{2}(2*5)-log_{2}5+3^{log_{3}3-log_{3}4}=\\\\log_{2}2+log_{2}5-log_{2}5+3^{log_{3}\frac{3}{4}}=\\\\1+\frac{3}{4}=\frac{4+3}{4}=\frac{7}{4}$

Observatii

$log_{a}{b*c}=log_{a}b+log_{a}c\\\\log_{a}\frac{b}{c}=log_{a}b-log_{a}c\\\\a^{log_{a}b}=b$