Question

Sa se stabileasca semnul expresiilor:
a) $log_{6} 7$·$log_{2} 3$
b)$log_{4} \frac{1}{5}$·$log_{3} 2$·$log_{\frac{1}{2} } \frac{1}{3}$
c)$log_{5} \frac{1}{2}$·$log_{\frac{1}{3} } 7$·$lg_{\frac{1}{10} }$

Answer 1

Explicație pas cu pas:

a) log(6) 7 * log(2)  3  >0

b) log(4)  1/5  * log(3) 2 * log(1/2)  1/3<0

c) log(5) 1/2 * log(1/3) 7 * lg(1/10)<0

de ce?

fie avem log(a) b unde a∈(0,+∞)-{1} si b∈(0,+∞)

deci: log(a) b>0 daca a∈(0,1) b∈(0,1) respectiv a∈(1,+∞) b∈(0,+∞)

si: log(a) b<0 daca a∈(0,1) , b∈(1,+∞) rspectiv a∈(1,+∞) , b∈(0,1)

Bafta!