To solve this inequality, we can let (a = 0.1^x). This allows us to rewrite the inequality as:
[a^3 - 3a^2 + 3a - 1 > 0]
Now, let's factor this expression using the binomial theorem:
[(a - 1)^3 > 0]
The inequality is true for (a > 1), which means (0.1^x > 1) is the solution. However, this is not possible because the base of a power cannot be less than 0 and greater than 1. Thus, the given inequality has no solution.
To solve this inequality, we can let (a = 0.1^x). This allows us to rewrite the inequality as:
[a^3 - 3a^2 + 3a - 1 > 0]
Now, let's factor this expression using the binomial theorem:
[(a - 1)^3 > 0]
The inequality is true for (a > 1), which means (0.1^x > 1) is the solution. However, this is not possible because the base of a power cannot be less than 0 and greater than 1. Thus, the given inequality has no solution.