Oblicz √a*b*c jeżeli: a=log(w podstawie 3)4 b=log(w podstawie 5)81 c=log(w podstawie 4)5 Oblicz √a*b*c jeżeli: log(w podstawie 2)6=a log(w podstawie 6)8=b log(w podstawie 8)32=c

[latex]a = log(3)4 = 2log(3)2 [/latex] [latex]b = log(5)81 = 4log(5)3[/latex] [latex]c = log(4)5= frac{1}{2}log(2)5[/latex] [latex] sqrt{2log(3)2*4log(5)3*frac{1}{2}log(2)5} =[/latex] [latex] sqrt{4 frac{1}{log(2)3} *log(5)3* frac{1}{log(5)2} } =[/latex] [latex] sqrt{4 frac{1}{log(2)3} * frac{log(5)3}{log(5)2} } =[/latex] [latex] sqrt{4 frac{1}{log(2)3} * log(2)3} = sqrt{4 frac{ log(2)3}{log(2)3} } =sqrt{4*1 } = sqrt{4} =2[/latex] [latex]a = log(2)6[/latex] [latex]b=log(6)8[/latex] [latex]c= log(8)32[/latex] [latex] sqrt{log(2)6*log(6)8*log(8)32} = sqrt{ frac{1}{log(6)2} *log(6)8* frac{5}{3} log(2)2} =[/latex] [latex] sqrt{ frac{log(6)8}{log(6)2} * frac{5}{3} *1} = sqrt{log(2)8 * frac{5}{3} *1} = sqrt{3* frac{5}{3} *1}= sqrt{5} [/latex]