Exponential inequality

[Guest]

Can you explain me how to solve this please?
5^(1/x)<1/25 Don't use logarithms.

[Guest]

[tex]\frac{1}{25} = \frac{1}{5^2} = 5^{-2}[/tex]

[tex]5^{\frac{1}{x}}<\frac{1}{25}[/tex]
[tex]5^{\frac{1}{x}}<5^{-2}[/tex]

[tex]\frac{1}{x}<-2[/tex]

[tex]\frac{1}{x} + 2<0[/tex]

[tex]\frac{1+2x}{x}<0[/tex]

we have 3 intervarlas [tex](-\infty , -\frac{1}{2}), (-\frac{1}{2}, 0), (0, \infty)[/tex]

Solutions are [tex](-\infty , -\frac{1}{2}) \cup (0, \infty)[/tex]

[Guest]

Is it clear?