First slide

Theory of equations

Question

If $7^{\log 7 (x^{2} - 4 x + 5)} = x - 1, x$ may have value

Moderate

Solution

We have
$7^{\log 7 (x^{2} - 4 x + 5)} = x - 1$
$\Rightarrow x^{2} - 4 x + 5 = x - 1 \Rightarrow x^{2} - 5 x + 6 = x - 1 \Rightarrow x = 2, 3$

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