Równianie logarytmiczne
michal1103: Rozwiąż równanie:
x3−log(x/3)=900
2 lis 19:30
Artur ..... :
| | logx (3000) − logxx | |
3 − log (x/3) = log (1000/(x/3)) = log (3000/x) = |
| = |
| | logx 10 | |
| | logx(3000) − 1 | | logx(30) + 2logx(10) − 1 | |
= |
| = |
| |
| | logx 10 | | logx(10) | |
900 = x
logx (900) = x
2logx (30)
| logx(30) + 2logx(10) − 1 | |
| = 2logx (30) |
| logx(10) | |
log
x(30) + 2log
x(10) − 1 = 2log
x (10)log
x (30)
log
x(30) + 2log
x(10) − 1 − 2log
x (10)log
x (30) = 0
(log
x(30) − 1) − 2log
x(10)(log
x(30) −1) = 0
(1−2log
x(10))(log
x(30)−1) = 0
1−2log
x(10) = 0 ⋁ log
x(30)−1 = 0
log
x(10) = 1/2 ⋁ log
x(30) = 1
√x = 10 ⋁ x
1 = 30
x= 100 ⋁ x = 30
2 lis 20:07
Eta:
x>0
logarytmujemy obustronnie logarytmem dziesiętnym
logx*(3−logx+log3)= 2+2log3 , podstawiam logx=t
3t−t2+t*log3= 2+2log3
t2−(3+log3)*t+2(1+log3)=0
Δ= (log3−1)2 , √Δ= log3−1
t= log3+1 v t= 2
to: logx= log30 v logx= 2 ⇒ x= 30 v x= 100
2 lis 21:00