[latex]Dziedzina:\3^{x+1}+1>0 land (9^x-2)>0\3^{x+1}>-1 -zawsze prawda land \ 9^x>2\log_39^x>log_32\xlog_39>log_32 |:log_39\x>frac{log_32}{2}\x>frac12log_32\x>log_3sqrt2[/latex] [latex]log_2(3^{x+1}+1)>1+log_2(9^x-2)\log_2(3^{x+1}+1)>log_22+log(3^{2x}-2)\log_2(3^{x+1}+1)>log_2(2*3^{2x}-4)\3*3^{x}+1>2*3^{2x}-4\3^x = a ; a>0\3a+1>2a^2-4\2a^2-3a-5 <0\Delta = (-3)^2-4*2*(-5) = 9+40 = 49\sqrtDelta = 7\a_1 = frac{3-7}{4} = -1<0\a_2 = frac{3+7}{4} = frac{10}{4} = 2,5\a in (0;2,5)\gdy a =2,5 \ 3^x = 2,5 \log_33^x = log_32,5\xlog_33 = log_32,5\x = log_32,5[/latex] Uwzględniając dziedzinę: [latex]x in(log_3sqrt2; log_32,5)[/latex]
