Question

Đã trả lời bởi chuyên gia

Answer 1

1)

$\frac{3^{x}}{27} = 3 \Leftrightarrow 3^{x} = 3.27 \Leftrightarrow 3^{x} = 3^{4} \Leftrightarrow x = 4 2) x^{2002} = x \Rightarrow x = 1 h o ặ c x = 0 3) 5^{2 x} {.55}^{x} = 625 \Leftrightarrow {(5^{2})}^{X} . 55^{X} = 625 \Leftrightarrow {(25.55)}^{x} = 625 \Leftrightarrow 1375^{x} = 625 \Rightarrow x = \log_{1375} 625 4) 9^{x - 1} = 9 \Leftrightarrow 9^{x - 1} = 9^{1} \Leftrightarrow x - 1 = 1 \Leftrightarrow x = 2 5) \frac{2^{x}}{2^{5}} = 1 \Leftrightarrow 2^{x - 5} = 1 \Leftrightarrow x - 5 = 0 \Leftrightarrow x = 5 6) {(2 x + 1)}^{3} = 125 \Leftrightarrow {(2 x + 1)}^{3} = 5^{3} \Leftrightarrow 2 x + 1 = 5 \Leftrightarrow 2 x = 4 \Leftrightarrow x = 2 7) 2014^{2 x - 6} = 1 \Leftrightarrow 2 x - 6 = 0 \Leftrightarrow 2 x = 6 \Leftrightarrow x = 3 9) {(2 x - 3)}^{2} = 81 \Leftrightarrow {(2 x - 3)}^{2} = 9^{2} \Leftrightarrow 2 x - 3 = 9 \Leftrightarrow 2 x = 12 \Leftrightarrow x = 6 10) x^{199} = x^{2} \Rightarrow x = 0 h o ặ c x = 1 10) 5^{x + 2} = 625 \Leftrightarrow 5^{x + 2} = 5^{4} \Leftrightarrow x + 2 = 4 \Leftrightarrow x = 2 11) \frac{5^{2 x} . 5^{x + 1}}{5} = 125 \Leftrightarrow 5^{2 x + x + 1 - 1} = 5^{3} \Leftrightarrow 5^{3 x} = 5^{3} \Leftrightarrow 3 x = 3 \Leftrightarrow x = 1 12) 3^{x} + 3^{x + 1} + 3^{x + 2} = 243.39 \Leftrightarrow 3^{x} + 3 . 3^{x} + 9 . 3^{x} = 3^{5} . 3.13 \Leftrightarrow 3^{x} . (1 + 3 + 9) = 3^{6} . 13 \Leftrightarrow 13 . 3^{x} = 13 . 3^{6} \Leftrightarrow 3^{x} = 3^{6} \Leftrightarrow x = 6$

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Answer 2

1)

$\frac{3^{x}}{27} = 3 \Leftrightarrow 3^{x} = 3.27 \Leftrightarrow 3^{x} = 3^{4} \Leftrightarrow x = 4 2) x^{2002} = x \Rightarrow x = 1 h o ặ c x = 0 3) 5^{2 x} {.55}^{x} = 625 \Leftrightarrow {(5^{2})}^{X} . 55^{X} = 625 \Leftrightarrow {(25.55)}^{x} = 625 \Leftrightarrow 1375^{x} = 625 \Rightarrow x = \log_{1375} 625 4) 9^{x - 1} = 9 \Leftrightarrow 9^{x - 1} = 9^{1} \Leftrightarrow x - 1 = 1 \Leftrightarrow x = 2 5) \frac{2^{x}}{2^{5}} = 1 \Leftrightarrow 2^{x - 5} = 1 \Leftrightarrow x - 5 = 0 \Leftrightarrow x = 5 6) {(2 x + 1)}^{3} = 125 \Leftrightarrow {(2 x + 1)}^{3} = 5^{3} \Leftrightarrow 2 x + 1 = 5 \Leftrightarrow 2 x = 4 \Leftrightarrow x = 2 7) 2014^{2 x - 6} = 1 \Leftrightarrow 2 x - 6 = 0 \Leftrightarrow 2 x = 6 \Leftrightarrow x = 3 9) {(2 x - 3)}^{2} = 81 \Leftrightarrow {(2 x - 3)}^{2} = 9^{2} \Leftrightarrow 2 x - 3 = 9 \Leftrightarrow 2 x = 12 \Leftrightarrow x = 6 10) x^{199} = x^{2} \Rightarrow x = 0 h o ặ c x = 1 10) 5^{x + 2} = 625 \Leftrightarrow 5^{x + 2} = 5^{4} \Leftrightarrow x + 2 = 4 \Leftrightarrow x = 2 11) \frac{5^{2 x} . 5^{x + 1}}{5} = 125 \Leftrightarrow 5^{2 x + x + 1 - 1} = 5^{3} \Leftrightarrow 5^{3 x} = 5^{3} \Leftrightarrow 3 x = 3 \Leftrightarrow x = 1 12) 3^{x} + 3^{x + 1} + 3^{x + 2} = 243.39 \Leftrightarrow 3^{x} + 3 . 3^{x} + 9 . 3^{x} = 3^{5} . 3.13 \Leftrightarrow 3^{x} . (1 + 3 + 9) = 3^{6} . 13 \Leftrightarrow 13 . 3^{x} = 13 . 3^{6} \Leftrightarrow 3^{x} = 3^{6} \Leftrightarrow x = 6$

Answer 3

`1 ) 3^x/27 = 3`

`=> 3^x = 3.27`

`=> 3^x = 81`

`=> 3^x = 3^4`

`=>x =4`

Vậy `x = 4`

`2 ) x^2002 = x`

`=> x^2002 - x = 0`

`=> x . (x^2001 -1) =0`

`=> [(x=0) , (x^2001 -1 =0):}`

`=> [(x=0) , (x^2001 = 1):}`

`=> [(x=0) , (x=1):}`

Vậy `x in {0;1}`

`3 ) 5^(2x) .5 . 5^x = 625` ( Đề mình nghĩ )

`=> 5^(2x+1+x) = 5^4`

`=> 2x + 1 + x = 4`

`=> (2+1)x = 4-1`

`=> 3x = 3`

`=> x = 3:3`

`=> x =1`

Vậy `x = 1`

`4 ) 9^(x-1) = 9`

`=> 9^(x-1) =9^1`

`=> x - 1= 1`

`=> x = 1+1`

`=> x =2`

Vậy `x = 2`

`5 ) 2^x/2^5 = 1`

`=> 2^x = 1.2^5`

`=> 2^x = 2^5`

`=> x = 5`

Vậy `x = 5`

`6 ) (2x+1)^3 = 125`

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

`=> 2x+1 = 5`

`=> 2x =5-1`

`=> 2x = 4`

`=> x = 4:2`

`=> x = 2`

Vậy `x = 2`

`10 ) 5^(x+2) = 625`

`=> 5^(x+2) = 5^4`

`=> x +2=4`

`=> x = 4-2`

`=> x = 2`

Vậy `x = 2`

`7) 2014 ^ (2x - 6) = 1`

`<=>2x-6=0`

`<=>x=3`

`8) 3 ^ x + x ^ 2 = 1`

`<=> x^2=1-3^x<1`

`x^2<1`

`=>x^2=0`

`=>x=0`

`=>x=1-3^0=1-1=0(tm)``

Vậy` x=0`

`9) (2x - 3) ^ 2 = 81`

`<=> 2x-3=±9`

`=>2x=12;-6`

`=>x=6;-3`

`10) x ^ 199 = x ^ 2`

`x^199=x^2`

`=>x^197=1`

`=>x=1`

`11) (5 ^ (2x) * .5 ^ (x + 1)) / 5 = 125`

`=>5^(2x)*5^(x+1)=5^4`

`=>2x+x+1=4`

`=>3x=3`

`=>x=1`

`12) 3 ^ x + 3 ^ (x + 1) + 3 ^ (x + 2) = 243.39`

`3^x+3^(x+1)+3^(x+2)=3^5*3*13`

`3^x+3^(x+1)+3^(x+2)=3^6*13`

`3^x(1+3+3^2)=3^6*13`

`=>3^x*13=3^6*13`

`=>x=6`

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Answer 4

`1 ) 3^x/27 = 3`

`=> 3^x = 3.27`

`=> 3^x = 81`

`=> 3^x = 3^4`

`=>x =4`

Vậy `x = 4`

`2 ) x^2002 = x`

`=> x^2002 - x = 0`

`=> x . (x^2001 -1) =0`

`=> [(x=0) , (x^2001 -1 =0):}`

`=> [(x=0) , (x^2001 = 1):}`

`=> [(x=0) , (x=1):}`

Vậy `x in {0;1}`

`3 ) 5^(2x) .5 . 5^x = 625` ( Đề mình nghĩ )

`=> 5^(2x+1+x) = 5^4`

`=> 2x + 1 + x = 4`

`=> (2+1)x = 4-1`

`=> 3x = 3`

`=> x = 3:3`

`=> x =1`

Vậy `x = 1`

`4 ) 9^(x-1) = 9`

`=> 9^(x-1) =9^1`

`=> x - 1= 1`

`=> x = 1+1`

`=> x =2`

Vậy `x = 2`

`5 ) 2^x/2^5 = 1`

`=> 2^x = 1.2^5`

`=> 2^x = 2^5`

`=> x = 5`

Vậy `x = 5`

`6 ) (2x+1)^3 = 125`

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

`=> 2x+1 = 5`

`=> 2x =5-1`

`=> 2x = 4`

`=> x = 4:2`

`=> x = 2`

Vậy `x = 2`

`10 ) 5^(x+2) = 625`

`=> 5^(x+2) = 5^4`

`=> x +2=4`

`=> x = 4-2`

`=> x = 2`

Vậy `x = 2`

`7) 2014 ^ (2x - 6) = 1`

`<=>2x-6=0`

`<=>x=3`

`8) 3 ^ x + x ^ 2 = 1`

`<=> x^2=1-3^x<1`

`x^2<1`

`=>x^2=0`

`=>x=0`

`=>x=1-3^0=1-1=0(tm)``

Vậy` x=0`

`9) (2x - 3) ^ 2 = 81`

`<=> 2x-3=±9`

`=>2x=12;-6`

`=>x=6;-3`

`10) x ^ 199 = x ^ 2`

`x^199=x^2`

`=>x^197=1`

`=>x=1`

`11) (5 ^ (2x) * .5 ^ (x + 1)) / 5 = 125`

`=>5^(2x)*5^(x+1)=5^4`

`=>2x+x+1=4`

`=>3x=3`

`=>x=1`

`12) 3 ^ x + 3 ^ (x + 1) + 3 ^ (x + 2) = 243.39`

`3^x+3^(x+1)+3^(x+2)=3^5*3*13`

`3^x+3^(x+1)+3^(x+2)=3^6*13`

`3^x(1+3+3^2)=3^6*13`

`=>3^x*13=3^6*13`

`=>x=6`

Answer 5

1)

3x27=3⇔3x=3.27⇔3x=34⇔x=42)x2002=x⇒x=1 hoặc x=03)52x.55x=625⇔52X.55X=625⇔25.55x=625⇔1375x=625⇒x=log13756254)9x-1=9⇔9x-1=91⇔x-1=1⇔x=25)2x25=1⇔2x-5=1⇔x-5=0⇔x=56)(2x+1)3=125 ⇔(2x+1)3=53 ⇔2x+1=5⇔2x=4⇔x=27)20142x-6=1⇔2x-6=0⇔2x=6⇔x=39)(2x-3)2=81⇔(2x-3)2=92⇔2x-3=9⇔2x=12⇔x=610)x199=x2⇒x=0hoặcx=110)5x+2=625⇔5x+2=54⇔x+2=4⇔x=211)52x.5x+15=125⇔52x+x+1-1=53⇔53x=53⇔3x=3⇔x=112)3x+3x+1+3x+2=243.39⇔3x+3.3x+9.3x=35.3.13⇔3x.(1+3+9)=36.13⇔13.3x=13.36⇔3x=36⇔x=6

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