# DISEQUAZIONI LOGARITMICHE E ESPONENZIALI

 $3·\sqrt[3]{{5}^{x+1}}>\frac{2}{\sqrt{{3}^{x-1}}}$ (R) $\frac{2}{{3}^{x+2}}<\frac{3}{{2}^{1-x}}$ (R) ${4}^{x}-3·{2}^{x+2}+27\le 0$ (R) ${4}^{-x}-3·\frac{1}{{2}^{x}}+2\ge 0$ (R) ${3}^{x+1}+{3}^{x-1}>{4}^{x}+{2}^{2x-1}$(R) ${\mathrm{log}}_{3}^{2}\left(x-1\right)-3·{\mathrm{log}}_{3}\left(x-1\right)-4>0$ (R) $\frac{{\mathrm{log}}_{2}x-1}{2-{\mathrm{log}}_{2}x}>2$ (R) ${\mathrm{log}}_{2}\frac{\sqrt{{x}^{2}-1}}{x+4}\ge {\mathrm{log}}_{4}\frac{{\left(4+x\right)}^{2}}{{x}^{2}-1}$ (R) $\frac{{e}^{2x}-{e}^{x}}{2·{e}^{2x}-5·{e}^{x}+2}>-1$ (R) $\frac{\mid \mathrm{ln}x\mid }{{\left(\mathrm{ln}x-1\right)}^{2}}\le \frac{1}{2}$ (R) ${11}^{x}<18·{11}^{-x}+3$ (R) $\mathrm{ln}x+\frac{2}{\mathrm{ln}x}-3\le 0$ (R) ${3}^{x+1}\ge {2}^{1-x}$ (R) $\frac{\mathrm{ln}x-9}{3-\mathrm{ln}\mid x\mid }>0$ (R) ${\mathrm{log}}_{\frac{1}{2}}{\mathrm{log}}_{\frac{1}{2}}\left(x+\frac{3}{2}\right)\le 1$ (R) $\frac{\mathrm{log}x-1}{\mathrm{log}\left(x-1\right)}\le 0$ (R) $3·\left({\mathrm{log}}_{3}x+{\mathrm{log}}_{x}3\right)\ge 10$ (R) ${4}^{x}+10>7·{2}^{x}$ (R) $\frac{{7}^{3+x}}{5}>4·{3}^{5x}$ (R) $\frac{{\mathrm{log}}_{3}\mid 2x+3\mid -3}{{\mathrm{log}}_{3}x}>0$ (R) ${\mathrm{log}}_{2}{\mathrm{log}}_{3}\left(x+4\right)>0$ (R) $\sqrt{{5}^{x-1}}<9·{3}^{2x}$ (R) $\frac{{3}^{x}-1}{{3}^{-x}-3}\ge 0$ (R) ${\mathrm{log}}_{2}{\mathrm{log}}_{\frac{1}{2}}\left(x-6\right)<0$ (R) $40-9·{2}^{x}>20-{2}^{2-x}$ (R) $\frac{\mid {2}^{x}-4\mid -{2}^{x}+4}{{5}^{x}-2}>0$ (R) $\mathrm{ln}{\left(3-x\right)}^{2}-2·\mathrm{ln}\left(4+x\right)<0$ (R) $24·{5}^{x}\ge 5·{6}^{x+1}$ (R) $\frac{\mathrm{ln}\left(3-x\right)-\mathrm{ln}2x}{\mid \mathrm{ln}\left(3-x\right)\mid }\ge 0$ (R) $\frac{1}{\mathrm{log}x}-3·\mathrm{log}x<2$ (R) $\frac{1-{3}^{x}}{{4}^{x-2}-{2}^{x}}>0$ (R) $\mathrm{log}\left({x}^{2}+17x+16\right)<2$ (R) ${\left(\frac{2}{5}\right)}^{x}-{\left(\frac{5}{2}\right)}^{-2x}<2$ (R) $\sqrt{25-{5}^{x}}\le {5}^{x}-5$ (R)