PROSZĘ O POMOC 1. Oblicz wartość wyrażeń a) log3 27 - log2 8= b) log4 1+ log5 25 = c) log3 pierwiastek z 3 + log6 pierwiastek z 6 = 2. Oblicz x a) log256 4 = x b) x=log5 9+ 2 (log5 1 - log5 3) c) logx 216=3

[latex]1\ a) log_{3}27-log_{2}8=log_{3}3^3-log_{2}2^3 = 3-3=0\ b) log_{4}1+log_{5}{25}=log_{4}4^0+log_{5}5^2=0+2=2\ \ [/latex] [latex]2\ a) log_{256}4=x\ 256^x=4\ (4^4)^x=4^1\ 4^{4x}=4^1\ 4x=1\ x=frac{1}{4}\ \ [/latex] [latex]b) x=log_{5}9+2(log_{5}1-log_{5}3)=log_{5}9-2(log_{5}frac{1}{3})= \ =log_{5}9-log_{5}(frac{1}{3})^2= log_{5}9-log_{5}frac{1}{9}=log_{5}(frac{9}{frac{1}{9}})= log_{5}81[/latex] [latex]c)\ log_{x}216=3\ x^3=216\ x^3=6^3\ x=6[/latex]