Question

log11 din 3 * log7 din 5 = log7 din 3 * log11 din 5

Answer 1

$\log_{11}3\cdot\log_75=\frac{\log_73}{\log_711}\cdot\frac{\log_{11}5}{\log_{11}7}=\frac{\log_73\cdot\log_{11}5}{\log_711\cdot\log_{11}7}=\frac{\log_73\cdot\log_{11}5}{\frac{1}{\log_{11}7}\cdot\log_{11}7}=\\=\log_73\cdot\log_{11}5}$
Am folosit:
[tex]\log_aA=\frac{\log_bA}{\log_ba}\\ \log_ba=\frac{1}{\log_ab}[/tex]