Question

Please help me with this logarithmic equation. How do I solve it?

Answer 1

No real solution.

Explanation:

The feasible solutions are `(x > 0) nn (x(x^2-8x+25) > 0)` but for `x > 0` we have `x^2-8x+25 > 0` with minimum at `x =4` with value `4^2-8 cdot 4 + 25 = 9`

Now `log(x^3-8x^2+25x)-log(x)=log(x^2-8x+25)=1` or

`x^2-8x+25 = e` but as we saw previously `x^2-8x+25 ge 9` so no real solutions for this equation.