Question

log2(3x-1)=2
lg(2x+1)=0
ln(4x-1)=1
log3(5x-2)=2

Answer 1

x=5/3
x=0
x=(e+1)/4
x=11/5

Answer 2

log2(3x-1)=2

Conditii de existenta
Exericitul 1

3x-1>0
3x>1

x>1/3 x apartin. (1/3 infinit )

Conform formulei [tex]log_{a}b=c a^c=b [/tex]

[tex]2^2=3x-1 4=3x-1 4-3x+1=0 -3x+5=0 -3x=-5 /(-1) 3x=5 x=5/3[/tex] apartine intervalui (1/3 infinit )


Exericitiul 2

Conditii de existenta

2x+1>0
2x>-1
 
x>-1/2  x apartine lui (-1/2 infinit )

lg=logaritm zecimal din baza 10

[tex]10^0=2x+1 1=2x+1 1-2x-1=0 -2x=0 x=0[/tex] 0 nu apartine  lui (-1/2,infinit)


Exericitul 3

lnx=logartm in baza e din x
adica e(constanta lui euler(aproximativ 2,71) la o putere necunoscuta
  
Conditii de existenta

4x-1>0
4x>1
x>1/4  x apartine lui (1/4 infinit)

[tex]e^1=4x-1 x= e+1/4[/tex]    apartine lui (1/4 infinit )


Exercitiul 4

Conditii de existena

5x-2>0
5x>2

x>5/2 x apartine int.(5/2 infinit)
 
[tex]3^2=5x-2 9=5x-2 9-5x+2=0 -5x+11=0 -5x=-11 /(-1) 5x=11 x=11/5[/tex]  apartine intervalului (5/2 infinit )