$7^{\log _7\left(x^2-4 x+5\right)}=x-1$, x may have values:
Answer & explanation
Correct answer: option 1
We have $7^{\log _7\left(x^2-4 x+5\right)}=x-1$
$\Rightarrow x^2-4 x+5=x-1\left(∵ a^{\log _a x}=x\right)$
⇒ (x − 3)(x − 2) = 0 ⇒ x = 2, 3
Hence (1) is the correct answer.