a] log5 x = 3log5 2 log5 x = log5 2³ x=2³=8 b]log7 x = 2log7 3 log7 x = log7 3² x=3²=9 c]log1/2 x = 3log1/2 5 log1/2 x=log1/2 5³ x=5³=125 d]log0.1 x=6log0.1 10 log0,1 x=log0,1 10^6 x=10^6=1000000 e]log x = 2log pierwiastek 2 log x = log(√2)²\ x=(√2)²=2 f]log x = 4log pierwiastek 3 log x = log(√3)^4=3²=9
[latex]Dziedzina do wsztystkich przykladow:xinmathbb{R^+}\\Zastosowanie wzoru:\dla a > 0 wedge a eq1 wedge b > 0 wedge cinmathbb{R}\log_ab^c=ccdot log_ab\\a) log_5x=3log_52\\log_5x=log_52^3iff x=2^3 o x=8in D\\b) log_7x=2log_73\\log_7x=log_73^2iff x=3^2 o x=9in D[/latex] [latex]c) log_frac{1}{2}x=3log_frac{1}{2}5\\log_frac{1}{2}x=log_frac{1}{2}5^3iff x=5^3 o x=125in D\\d) log_{0,1}x=6log_{0.1}10\\log_{0,1}x=log_{0,1}10^6iff x=10^6 o x=1000 000in D\\e) logx=2logsqrt2\\logx=log(sqrt2)^2iff x=(sqrt2)^2 o x=2in D\\f) logx=4logsqrt3\\logx=log(sqrt3)^4iff x=(sqrt3)^4 o x=3^2 o x=9in D[/latex]
