wykaż że jeśli : [latex]a= log_{3}15 [/latex] to [latex] log_{3} sqrt{5} = frac{a-1}{2} [/latex] Proszę o wszystkie obliczenia/ Dam NAJJ

log_3 5 + log_3 3 = a log _3 5 = a -1  2log_3 √5 = a - 1 log _3 √5 = (a -1)/2  q.e.d.

[latex]log_3 sqrt{5} = log_3 5^{frac{1}{2}} = frac{1}{2}log_3 5 = frac{1}{2} (log_3 5 + 1 - 1) = frac{1}{2} (log_3 5 + log_33 - 1) \ = frac{1}{2}(log_3 (5 imes 3) - 1) = frac{1}{2}(log_3 15 - 1) =\ = frac{log_3 15 - 1}{2} = frac{a - 1}{2} .[/latex]