Question

Demonstrați că
$log_{5}24 + log_{5}3 = 3 log_{5}2 + log_{5}45 - 1$

Answer 1

[tex]L.H.S.:\log_53+\log_524=\log_572\\ R.H.S.:3\log_52+\log_545-1=\log_52^3+\log_545-\log_55=\\ =\log_58+\log_545-\log_55=\log_5\dfrac{8\cdot 45}{5}=\log_5 72\\ \text{Asadar relatia este adevarata.}[/tex]