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Pati: Oblicz log2 √−ab wiedząc, że log(−a) 2=2 i log16 b=0,75.
2 paź 18:35
Basia:
log
(−a)2 = 2 ⇔ (−a)
2 = 2 ⇔ a
2 = 2 ⇔ a = ± 2
1/2
log
16b =
34 ⇔ b=16
3/4 ⇔ b = (2
4)
3/4 ⇔ b= 2
3
−ab jest pod pierwiastkiem ⇒ −ab≥0 ⇒ ab≤0 ⇒ a= −2
1/2 i b = 2
3
log
2 √−ab = log
2(−ab)
1/2 =
12*log
2(2
1/2*2
3) =
12*log
22
7/2 =
12*
72 =
74
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
inny sposób
log
2√−ab = log
2(−ab)
1/2 =
12*log
2(−ab) =
12*[ log
2(−a) + log
2b ] =
| 1 | | log−a(−a) | | log16b | |
| *[ |
| + |
| ] = |
| 2 | | log−a2 | | log162 | |
| 1 | | 1 | | 3 | | 4 | |
| *[ |
| + |
| * |
| ] = ..... |
| 2 | | 2 | | 4 | | 1 | |
policz do końca
2 paź 18:51