Oblicz x: 1) [latex]log _{2} x=log _{2} 64-log _{2} 2+5log _{2}1 [/latex] 2)  [latex]log_{4}log _{2} log_{3}(x-1)= frac{1}{2} [/latex]

1. Dziedzina x>0 [latex] log _{2} x=log _{2} 64-log _{2} 2+5log _{2}1 \ \ log _{2} x=log _{2} (64:2)+log _{2}1^5 \ \ log _{2} x=log _{2} 32+log _{2}1 \ \ log _{2} x=log _{2}32 +0 \ \ log _{2} x=log _{2}32 \ \ x=32[/latex] 2. Dziedzina x>0 [latex]log_{4}log _{2} log_{3}(x-1)= frac{1}{2} \ \ log _{2} log_{3}(x-1)= 4^{frac{1}{2}} \ \ log _{2} log_{3}(x-1)=2 \ \ log_{3}(x-1)=2^2 \ \ log_{3}(x-1)=4 \ \ log_{3}(x-1)=4log_33 \ \ log_{3}(x-1)=log_33^4 \ \ log_{3}(x-1)=log_381 \ \ x-1=81 \ \ x=81+1 \ \ x=82[/latex]