Question

am nevoie de ajutor ca rog frumos

Answer 1

c) $\it lg^2x-3lgx+2=0$

$\it Notam\ \ lgx = t,\ iar\ ecuatia\ devine:$

$\it t^2-3t+2=0,\ \ t_1=1,\ \ t_2=2$

$\it t=1 \Rightarrow lgx=1 \Rightarrow x =10^1 \Rightarrow x=10.$

$\it t=2 \Rightarrow lgx=2\Rightarrow x=10^2 \Rightarrow x=100.$


d) $\it log_2(x^2-x-2) -log_2(2x-4) =1 \Longrightarrow log_2\dfrac{x^2-x-2}{2x-4} =1 \Longrightarrow$

$\it \Longrightarrow \dfrac{x^2-x-2}{2x-4} =2^1 \Longrightarrow \dfrac{(x+1)(x-2)}{2(x-2)} = 2 \Longrightarrow \dfrac{x+1}{2} =2\Longrightarrow$

$\it \Longrightarrow x+1=4 \Longrightarrow x =3.$