1) lgb = , = b ( > 0, 1), . . = b | = 3 |
2) lg = 1, ( > 0) | lg143143 = 1, |
3) lg1=0, ( > 0, 1) | 1g471=0 |
4) lg b = lg + 1g b ( > 0, 1, > 0, b > 0) | log14 2 + log147 = log14 (2 7) = 1g1414 = 1 |
5) lg = lg - 1g b | log3 75 log3 25 = log3 = log3 3 = 1 |
6) lg n = n lg ( > 0, > 0, 1) | log3 243 = log3 35 = 5log3 3 = 5 |
7) lg = ( > 0, > 0, 1, m > 0, m 1) | = log5 125 = log5 53 = 3lg5 5 = 3 |
8) log10 = lg (> 0) loge = ln ( >0) | lg 1000 = log10 1000 = log10 103 = 3 1n -5 = loge -5 = - 5 loge = -5 |
1. 5 ∙
. = b :
5 ∙ = 512 = 60.
: 60
2. log3 15 - 1g35 + 3
. ) lg - 1g b = lg , = b, lg = 1, :
log3 15 - 1g35 + 3 = lg33 + 5 = 1 + 5 = 6.
: 3.
3. : lg336 - 21g32.
. .
lg336 - 21g32 = lg3(32 ∙22) - 2lg32 = lg332 + lg322 - 2lg32 = 2lg33 + 2lg32 - 2lg32 = =21 = 2
g.
lg336 - 21g32 = lg336 - 1g322 = lg3 = lg3 9 = 2
:2.
4. 1g 0,3 7,5, 1g 0,3 5 = .
. 7,5 5 0,3:
7,5 = 25 0,3 = 52 ∙0,3 1g 0,3 7,5,
1g 0,3 7,5 = 1g 0,3 (52 ∙0,3) = 1g 0,3 52 +1g 0,3 0,3 = 21g 0,3 5 + 1 = 2 + 1
: 2 + 1.
1. 1g π(2 + 0,1) = 0.
. 2 + 0,1 = π0, . . 2+0,1 = 1, 2 = 0,9.
, 1,2 = , 1 2 = - ∙ = - 0,9.
: - 0,9.
2. !g5(2) = lg536 1g54?
1) [0; 4]; 2) (4; 10); 3) [10; 18]; 4) (18; 24).
. , : lg5(2) = lg5 , lg5(2) = 1g59. 2 = 9, , = 4,5. . .
4,5 (4; 10), 2
: 2.
3. ,
1g 0,4(5 - 2) - 1g 0,4 2 = 1.
1) (- ; -2); 2) [-2; 1]; 3) [1; 2]; 4) (2; + ).
. 1g 0,4(5 - 2) - 1g 0,4 2 = lg 0,4 . . lg 0,4 =1, = 0,4
= ; 25-10 = 4; -10 = - 21 = 2,1
: 4.
4. lg(4 3) = 2lg.
. lg(4 3) = 2lg
4 - 3 = 2,
|
|
> .
4 - 3 = 2 2 - 4 + 3 = 0; 1 = 1, 2 = 3; 1 > , 3 > , , 1 3 ; 1 + 3 = 4.
: 4.
1. ,
1) (0; 1); 2)(1;2); 3) (2; 3); 4) (3; 4).
. () = , :
= 5-1, 52(-) = 5-1 , , : 2(3 - ) = -1; 6 - 2 = -1, - 2 = -7, = 3,5
3,5 (3; 4), 4.
: 4.
2. ,
2 -1 + 2 +1 = 20.
1) (4; 5); 2) [3; 4]; 3) (2; 3); 4) [1; 2].
. 2 -1 + 2 +1 = 20; + 22 = 20; 2 + 4∙2 = 40; 5 2 = 40; 2 = 8; = 3;
[3;4].
: 2.
3. = 243.
. = 243; = 35; 2 - 1 = 5;
2=6; 1,2= 12 = = -6 | 2 6 = 0 12 = -6 ( ) |
: 1
().
1) (m)´ = m m-1 2) ()´ = 3) ´ = 4) ()´ = 5) ( )´ = 1n 6) (lnx)´ = 7) (lg)´ = | 8) (sin x)´ = cos x 9) (cos x)´ = - sin x 10) (tg x)´ = s2 = 11) (ctg x)´ = - cs2 = 12) (arcsin x)´ = 13) (s )´ = - |