Question

sa se rezolve in multimea numerelor reale ecuatiile logaritmice :
a) log4x=2
b)log2x=5
c)lg x=-2
d)log3(3x-1)=log3(2x+1)
e)log2(2x+5)=log2(x la a 2 a +3x+3)
f)log2(10-x)=2
g)log2(x-3)=0
h)log3(x la a 2 a -4x+4)=2

Answer 1

a) log4(x) = log4(16) => x = 16
b) log2(x) = log2 (2^5) => x = 32
c) lg x = lg (10^(-2)) => x = 1/ 100
d) 3x -1 =2x + 1 => x = 2
e) 2x + 5 = x^2 + 3x + 3 => x^2 +x - 2 = 0   delta = 1 + 8 =9 , radical din delta = 3, x1= (1-3)/2 = -1, x2 = (1+3)/2 = 2
f)log2(10-x)=log2(4) => 10-x=4 => x = 6
g) log2(x-3)=log2(1) => x -3 = 1 => x = 4
h)log3(x la a 2 a -4x+4)=log3(9) =>  x^2 -4x +4 = 9 => x^2 -4x - 5 = 0
delta = 16 + 20 = 36, radical din delta = 6 
x1=(4-6)/2= -1
x2 = (4+6)/2 = 5