a) [latex]log _{5} (x+5)=m[/latex] dziedzina: [latex]x>-5[/latex] [latex]5^m=x+5[/latex] [latex]x=5^m-5[/latex] 1. [latex]5^m-5>0[/latex] [latex]5^m>5[/latex] [latex]5^m>5^1[/latex] [latex]m>1[/latex] [latex]m in (1;+ infty )[/latex] 2. Z dziedziny: [latex]x>-5[/latex] [latex]5^m-5>-5[/latex] [latex]5^m>-5+5[/latex] [latex]5^m>0[/latex] Z 1 i 2 [latex]m in (1;+ infty )[/latex] ============================ b) [latex]log _{0,5} (x+4)= frac{m}{m+1}[/latex] dziedzina: [latex]x>-4[/latex] [latex]m eq -1[/latex] [latex]0,5^{ frac{m}{m+1}}=x+4[/latex] [latex]x=left( frac{1}{2} ight)^{ frac{m}{m+1}}-4[/latex] [latex]x=2^{-frac{m}{m+1}}-4[/latex] 1. [latex]2^{-frac{m}{m+1}}-4>0[/latex] [latex]2^{-frac{m}{m+1}}>4[/latex] [latex]2^{-frac{m}{m+1}}>2^2[/latex] [latex]-frac{m}{m+1}>2 / cdot (-1)[/latex] [latex]frac{m}{m+1}<-2[/latex] [latex]frac{m}{m+1}+2<0[/latex] [latex]frac{m}{m+1}+ frac{2(m+1)}{m+1}<0[/latex] [latex]frac{m+2(m+1)}{m+1}<0[/latex] [latex]frac{m+2m+2}{m+1}<0[/latex] [latex]frac{3m+2}{m+1}<0[/latex] [latex]frac{3left(m+ frac{2}{3} ight) }{m+1}<0[/latex] [latex]3left(m+ frac{2}{3} ight)(m+1)<0 /:3[/latex] [latex]left(m+ frac{2}{3} ight)(m+1)<0[/latex] Parabola z ramionami skierowanymi do góry [latex]m in left(-1;- frac{2}{3} ight)[/latex] 2. Z dziedziny: [latex]x>-4[/latex] [latex]2^{-frac{m}{m+1}}-4>-4[/latex] [latex]2^{-frac{m}{m+1}}>-4+4[/latex] [latex]2^{-frac{m}{m+1}}>0[/latex] [latex]-frac{m}{m+1}}>0 /:(-1)[/latex] [latex]frac{m}{m+1}<0[/latex] [latex]m(m+1)<0[/latex] Parabola z ramionami skierowanymi do góry [latex]m in left(-1;0 ight)[/latex] Z 1 i 2 [latex]m in left(-1;- frac{2}{3} ight)[/latex]
