Question

Excluzând exercitiile 1 și 5 vă rog.

Answer 1

$\it 2)\ 4^{x+3}=64 \Leftrightarrow 4^{x+3}=4^3 \Leftrightarrow x+3=3 \Leftrightarrow x=0\\ \\ 3)\ 2^{x^2+x+1}=8 \Rightarrow \ 2^{x^2+x+1}=2^3 \Rightarrow x^2+x+1=3|_{-3} \Rightarrow x^2+x-2=0 \Rightarrow \\ \\ \Rightarrow x^2-x+2x-2=0 \Rightarrow x(x-1)+2(x-1)=0 \Rightarrow (x-1)(x+2)=0\Rightarrow$

$\it \Rightarrow \begin{cases}\it x+2=0 \Rightarrow x_1=-2\\ \\ \it x-1=0\Rightarrow x_2=1\end{cases}$

Answer 2

2. 4^(x+3) = 4^3

x+3 = 3

x = 0

3. 2^(x²+x+1) = 2^3

x²+x+1 = 3

x²+x-2 = 0

Delta = 1-4*1*(-2) = 9

x1 = (-1+3)/2 = 2/2 = 1

x2 = -2

4. C.E. x-6>=0

√(x-6) = 5 | ( )²

x-6 = 25

x = 31 verifica conditia

6. C. E. x²-x+2 >0

√(x²-x+2) = 2 | ( )²

x²-x+2 = 4

x²-x-2 = 0

Delta = 1-4*1*(-2) = 9

x1 = (1+3)/2 = 2

x2 = (1-3)/2 = -1

Ambele solutii convin.

7. C. E. x+3 >0

log2 ( x+3) = log2 (16)

x+3 = 16

x = 13 verifica conditia

8. C.E. 2x-1>0

log3 (2x-1) = log3 (9)

2x-1 = 9

2x = 10

x = 5 verifica conditia