Question

Solutia ecuatiei 2^x+1 + 2^x+2=6*2^x

Answer 1

2^x+1+2^x+2=6*2^x

ASTA AI SCRIS, cf.ORDINII OPERATIILOR!!

2^x+2^x+3=6*2^x

3=6*2^x-2^x-2^x

3=4*2^x

2^x=(3/4)

x= log in baz 2 din (3/4)=

log in baza 2 din3 -log in baz 2 din4=log in baz 2 din3- 2

daca vroiai altceva trebuia sa fi pus in evidenta exponentii cu ajutorul parantezelor

2^(x+1) +2^(x+2)=6*2^x

2*2^x+4^2^x=6*2^x

6*2^x=6*2^x

IDENTITATE!!

adevarata ∀x∈R, domeniul de definitrie al lui 2^x...

S=R

Answer 2

$2^{x+1}+2^{x}+2=6\cdot2^{x}\\ \\2^{x+1}+2^{x}+2-6\cdot2^{x}=6\cdot2^{x}-6\cdot2^{x}\\ \\ -5\cdot 2^{x}+2^{x+1}+2=\\ \\-5\cdot 2^{x}+2^{x}\cdot2+2=\\ \\-3\cdot 2^{x}+2=\\ \\ -3 \cdot 2^{x}+2 +3 \cdot 2^{x}=0+3 \cdot 2^{x}\\ \\2=3 \cdot 2^{x}\\ \\ 2^{x}=\frac{2}{3}\\ \\ln 2^{x}= ln \frac{2}{3}\\ \\ \\x= \frac{ln \frac{2}{3}}{ln 2}$