Решить уравнение: 13^(logx(13))=x^4

ответ: 1) V13 2) 1/V13

Пошаговое объяснение:

x>0; x≠1;

обе части равенства положительны, можно их прологарифмировать по основанию, например, 13...

logx(13)*log13(13) = 4*log13(x)

замена: log13(x) = t (t ≠ 0)

1/t = 4t

4t^2 = 1

t^2 = 1/4

t1 = 0.5; t2 = -0.5

и тогда х1 = V13; x2 = 1/V13

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5(х-4)= х+8 
5х - 20 = х+8
5х - х = 8+20
4х = 28
х=28/4
х= 7
5(7-4) = 7 +8
5 * 3 = 15
15=15

9- 7(х+3) = 5 -6х
9  - 7х  - 21 = 5 -6х
-7х - 12 = 5-6х
-7х +6х = 5+12
-х=17
х=-17
9  -  7 *( - 17  + 3) =  5 -  6  *(-17)
9  -  7 *  (-14) = 5+102
9+98 = 107
107=107

19,6 +у = 7(1,2-у)
19,6 +у = 8,4 -7у
у +7у = 8,4  - 19,6
8у= -11,2
у= -11,2/8
у=-1,4
19,6 + (-1,4) = 7 *(1,2 - (-1,4))
18,2 = 7* (1,2+1,4)
18,2 = 7*2,6
18,2=18,2

0,4(6-4у) = 0,5(7-3у) - 1,9
2,4 - 1,6у = 3,5  - 1,5у  -1,9
-1,6у  +1,5у = 1,6 -2,4
-0,1у= -0,8
у= -0,8 / (-0,1)
у=8
0,4* (6- 4*8) = 0,5* (7  - 3*8) - 1,9
0,4 * (-26) = 0,5*(-17) -1,9
-10,4 = -8,5-1,9 
-10,4 = -10,4

3/4 * (1/6 * х   -1/3) = 2х - 11  1/2
3/4  *  1/6   * х    -  3/4   *  1/3  = 2х  - 11  1/2
1/8  *  х   -   1/4  = 2х   -  11,5
0,125х - 0,25 = 2х -11,5
0,125х  - 2х = -11,5 + 0,25
-1,875х = -11,25
х= -11,25 / (-1,875)
х= 6
3/4 * ( 1/6  *6  - 1/3) = 2*6 -11 1/2
3/4  *  (1-1/3) = 12  - 11 1/2
3/4  *   2/3   = 1/2
2/4 = 1/2
1/2=1/2