Question

Sa se calculeze log₅30-log₂₅36

Answer 1

$\displaystyle log_530-log_{25}36 \\ \\ Aducem~pe~log_{25}36~in~baza~5. \\ Formula~pentru~schimbarea~bazei~unui~logaritm~ : \boxed{ log_ab= \frac{log_cb}{log_ca} } .\\ log_{25}36= \frac{log_536}{log_525} = \frac{log_56^2}{log_55^2} = \frac{2log_56}{2log_55} = \frac{2log_56}{2} =log_56 \\ \\ log_530-log_{25}36=log_530-log_56= log_5 \frac{30}{6} = log_55=1$