Question

ПОМОГИТЕ! 1)log1\7(7-3x)=-2 2)log1\8(13-x)=-2 3)log1\4(9-5x)=-3 4)log1\2(6-x)=-5 5)log1\2(13-x)=-4

Answer 1

1) ОДЗ:  7 - 3х> 0⇒ -3x > -7⇒ x < 7/3
теперь решаем:
7 - 3х = (1/7)^-2
7 - 3x = 49
3x = -42
x = -14 (  входит в ОДЗ)
Ответ:  -14.
2)ОДЗ: 13 - х> 0⇒ -x > -13⇒ x < 13
теперь решаем:
13 - х = (1/8)^-2
13 - x = 64
x = - 51 ( в ОДЗ входит)
Ответ: -51.
3)ОДЗ:  9 - 5х> 0⇒ -5x > -9⇒ x < 9/5 = 1,8
теперь решаем:
9 - 5х = (1/4)^-3
9 - 5x = 64
5x = -55
x = -11 ( входит в ОДЗ)
Ответ: -11.
4)ОДЗ:  6 - х> 0⇒ -x > -6⇒ x <  6
теперь решаем:
6 - х = (1/2)^-5
6 - x = 32
x = -26(входит в ОДЗ)
Ответ: -26
5).ОДЗ:  13 - х> 0⇒ -x > -13⇒ x < 13
теперь решаем:
13 - х = (1/2)^-4
13 - x = 16
x = -3( в ОДЗ входит)
Ответ: -3.

Answer 2

Sure, I can help you solve these logarithmic equations.

1. log₁/₇(7-3x) = -2 Rewrite the equation in exponential form: 7-3x = 7⁻² 7-3x = 1/49 Solve for x: 7-3x = 1/49 -3x = 1/49 - 7 -3x = -6 96/49 x = 2 32/147

2. log₁/₈(13-x) = -2 Rewrite the equation in exponential form: 13-x = 8⁻² 13-x = 1/64 Solve for x: 13-x = 1/64 -x = 1/64 - 832/64 -x = -831/64 x = 831/64

3. log₁/₄(9-5x) = -3 Rewrite the equation in exponential form: 9-5x = 4⁻³ 9-5x = 1/64 Solve for x: 9-5x = 1/64 -5x = 1/64 - 576/64 -5x = -575/64 x = 115/64

4. log₁/₂(6-x) = -5 Rewrite the equation in exponential form: 6-x = 2⁻⁵ 6-x = 1/32 Solve for x: 6-x = 1/32 -x = 1/32 - 192/32 -x = -191/32 x = 191/32

5. log₁/₂(13-x) = -4 Rewrite the equation in exponential form: 13-x = 2⁻⁴ 13-x = 1/16 Solve for x: 13-x = 1/16 -x = 1/16 - 208/16 -x = -207/16 x = 207/16

Therefore, the solutions to the given equations are:

1. x = 2 32/147
2. x = 831/64
3. x = 115/64
4. x = 191/32
5. x = 207/16