Question

log 2 ( x^2-4) = log 2 ( x^2-3x+2)

Answer 1

$\\ \log _2\left(x^2-4\right)=\log _2\left(x^2-3x+2\right) \\ \boxed{\mathrm{Cand \:\ au \:\ aceasi \:\ baza \:\ }\log_b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right) = g\left(x\right)} \\ => x^2-4=x^2-3x+2 \\ => -3x+2-2=-4-2 \\ => \frac{-3x}{-3}=\frac{-6}{-3} \\ => x = 2 \\ Verificare: \\ log_2\:\left(\:2^2-4\right)\:=\:log\:_2\:\left(\:2^2-3\cdot 2+2\right) => Fals \\ Nu\:\ avem\:\ nici\:\ o\:\ solutie\:\ pentru\:\ care\:\ x \in \mathbb{R}$