Question

Решите уравнения или логарифмы

Answer 1

Пошаговое объяснение:

x-6=10

x=10+6

x=16

3x+4=4x+1

3x-4x=1-4

-x= -3

x=3

x³+2=10

x³=10-2

x³=8

x=³√8

x=2

1) log₄(60+x)=3

60+x=4³

x=64-60

x=4

2) log₃9=x

$3^{x} =9$

x=2

3)log₂(x²+8)=4

x²+8=2⁴

x²=16-8

x²=8

x=±√8=±2√2

4) log₄(x²+11)=2

x²+11=4²

x²=16-11

x²=5

x=±√5

5) log₇x=2

x=7²

x=49

6)log₅(x²+25)=3

x²+25=5³

x²=125-25

x=√100

x=±10

Answer 2

1)

x - 6 = 10

x = 16

2)

3x + 4 = 4x +1

x = 3

3)

x^3 + 2 = 10

x^3 = 8

x = 2

4)

log4(60 + x) = 3

ОДЗ: 60 + x > 0 => x > -60

log4(60 + x) = log4(4^3)

60 + x = 64

x = 4

5)

log3(9) = x

log3(3^2) = x

x = 2

6)

log2(x^2 + 8) = 4

ОДЗ: x^2 + 8 > 0 => x^2 > -8 => x Є R

log2(x^2 + 8)  = log2(2^4)

x^2 + 8 = 16

x^2 = 8

x = ±√8 = ±2√2

7)

log6(x^2+11) = 2

ОДЗ: x^2 + 11 > 0 => x^2 > -11 => x Є R

log6(x^2+11) = log6(6^2)

x^2 + 11 = 36

x^2 = 25

x = ±5

8)

log 7(x) = 2

ОДЗ : x>0

x = 7^2

x = 49

9)

log5(x^2+25) = 3

x^2 + 25 = 5^3

x^2 = -25 + 125

x^2 = 100

x = ±10