Oblicz x a) log log_{6} x = log_{6} 4 + log_{6} 9 b) log_{3} x = log_{3} 18 - log_{3} 2 c) log x = 2 log 5 + log4 d) log x = log80 - 3 log 2

[latex]a)log_6x=log_64+log_69 \log_6x=log_6(4 cdot 9) \log_6x=log_636 \x=36[/latex] ========================== [latex]b)log_3x=log_318-log_32 \log_3x=log_3( frac{18}{2}) \log_3x=log_39 \x=9 [/latex] ========================= [latex]c)logx=2cdot log5+log4 \logx=log5^2+log4 \logx=log(25cdot 4) \logx=log100 \x=100[/latex] ========================= [latex]d)logx=log80-3 cdot log2 \logx=log80-log2^3 \logx=log( frac{80}{8}) \logx=log10 \x=10 [/latex] ========================= Wykorzystane własności logarytmów: [latex]log_ab+log_ac=log_a(b cdot c) \\log_ab-log_ac=log_a( frac{b}{c}) \\n cdot log_ab=log_ab^n [/latex]