Równania logarytmiczne
Wiikuś: a)log4√x+12log4(x+4)=54
b)log4(x2−1)−12log4(x+4)2=112
c)log(x−5)2+log(x+6)2=2
4 paź 13:33
Janek191:
| | 5 | |
a) log4 √x + 0,5 log4 ( x + 4) = |
| ; x > 0 |
| | 4 | |
| 1 | | 5 | |
| log2 x0,5 + 0,5*0,5 log2 (x + 4) = |
| |
| 2 | | 4 | |
| 1 | | 1 | | 5 | |
| log2 x + |
| log2 ( x + 4) = |
| / * 4 |
| 4 | | 4 | | 4 | |
log
2 x + log
2 ( x + 4) = 5
log
2 x*(x + 4) = log
2 2
5
x
2 + 4 x = 32
x
2 + 4 x − 32 = 0
Δ = 16 − 4*1*(−32) = 16 + 128 = 144
√Δ = 12
| | − 4 − 12 | | − 4 + 12 | |
x = |
| < 0 − odpada lub x = |
| = 4 |
| | 2 | | 2 | |
Odp. x = 4
========
4 paź 15:29
Janek191:
c) log ( x − 5)2 + log ( x + 6)2 = 2 ; x > 5
log [ ( x − 5)2*( x + 6)2} = log 100
(x − 5)2*( x + 6)2 = 100
4 paź 15:36