Oblicz wartosc wyrazenia Log1/5 3·Log3 7·Log7 625

[latex]log_{frac{1}{5}} 3cdot log_3 7cdot log_7 625 = \ \ frac{log3}{logfrac{1}{5}}cdotfrac{log7}{log3}}cdotfrac{log625}{log7}= frac{1}{log5^{-1}}cdotfrac{1}{1}}cdotfrac{log5^4}{1}= \ \ frac{4log5}{-log5}=-4[/latex]

[latex]log_{frac{1}{5}} 3* log_3 7* log_7 625 = \ \Loa_aB= frac{Log_1_0B}{Log_1_0a} \ \ \ dfrac{log3}{logfrac{1}{5}}*dfrac{log7}{log3}}*dfrac{log625}{log7}= \ \ \dfrac{log ot3}{logfrac{1}{5}}*dfrac{log ot7}{log ot3}}*dfrac{log625}{log ot7}= dfrac{log625}{log frac{1}{5}} = \ \ \ dfrac{log5^4}{log5^{-1}} = dfrac{4log5}{-log5}=-4(dfrac{log5}{log5}) = oxed{-4} [/latex]