Question

Tìm số tự nhiên x biết rằng

2^x.4=128

x¹⁵=x

(2x+1)³=125

(x-5)⁴=(x-5)⁶

Answer 1

`@` `\text {Ans}`

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`2^x * 4 = 128`

`=> 2^x = 128 * 4`

`=> 2^x = 512`

`=> 2^x = 2^9`

`=> x = 9`

Vậy, `x = 9`

`x^15 = x`

`=> x^15 - x = 0`

`=> x(x^14 - 1) = 0`

`=>` TH1: `x = 0`

`TH2: x^14 - 1 = 0`

`=> x^14 = 1`

`=> x = 1`

Vậy, `x \in {0; 1}`

`(2x+1)^3 = 125`

`=> (2x+1)^3 = 5^3`

`=> 2x + 1 = 5`

`=> 2x = 5 - 1`

`=> 2x =4`

`=> x = 4 \div 2`

`=> x = 2`

Vậy,` x = 2.`

`(x - 5)^4 = (x-5)^6`

`=> (x-5)^4 - (x-5)^6 = 0`

`=> (x-5)^4 * [ 1 - (x-5)^2] = 0`

`=> - (x-6)(x-5)^4(x-4) = 0`

`TH1: (x - 5)^4 = 0`

`=> x - 5 = 0`

`=> x = 0 +5`

`=> x = 5`

`TH2: x - 6=0`

`=> x=6`

`TH3: x-4=0`

`=> x = 4`

Vậy, `x \in {4; 5; 6}`

Answer 2

a: =>2^x=32

=>x=5

b: =>x^15-x=0

=>x(x^14-1)=0

=>x=0; x=1;x=-1

c: =>2x+1=5

=>2x=4

=>x=2

d: =>(x-5)^4[(x-5)^2-1]=0

=>(x-5)(x-4)(x-6)=0

=>x=5;x=4;x=6