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

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

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Answer 1 · 2016-12-25T22:32:50

No real solution.

Explanation:

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

Now $log (x^{3} - 8 x^{2} + 25 x) - log (x) = log (x^{2} - 8 x + 25) = 1$ $log(x^3-8x^2+25x)-log(x)=log(x^2-8x+25)=1$ or

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

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

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Explanation:

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