Bài 6: Lũy thừa của một số hữu tỉ (tiếp theo...)

\(\left(x-3\right)^{x+2}-\left(x-3\right)^{x+2}.\left(x-3\right)^6=0\\ \left(x-3\right)^{x+2}\left[1-\left(x-3\right)^6\right]=0\\ \left[{}\begin{matrix}\left(x-3\right)^{x+2}=0\\1-\left(x-3\right)^6=0\end{matrix}\right.=>\left[{}\begin{matrix}x-3=0\\x-3=1\end{matrix}\right.=>x=3;x=4\)

`-> (x-3)^(x+2) . (1 - (x-3)^6) = 0`

`-> (x-3)^(x+2) = 0`

`-> x - 3 = 0`

`-> x = 3`

<=>1=(x-3)⁶

<=>x-3=1 hoặc x-3=-1

=>x=4 hoặc x=2

c) \(\dfrac{90^2}{15^2}=\left(\dfrac{90}{15}\right)^2=6^2=36\)

d) \(\dfrac{790^4}{79^4}=\left(\dfrac{790}{79}\right)^4=10^4=10000\)

\(=\dfrac{2^8.3^{16}}{3^{15}.2^6}=2^2.3=4.3=12\)

\(1\dfrac{3}{4}.\dfrac{-16}{7}\)
\(=\dfrac{7}{4}.\dfrac{-16}{7}\)
\(=-4\)
\(12:\dfrac{-6}{5}+\dfrac{1}{5}\)
\(=-10+\dfrac{1}{5}\)
\(=-\dfrac{49}{5}\)

`1 3/4 . -16/7=7/4.(-16/7)=-4. `
` 12: -6/5+1/5=-10+1/5=-49/5`

n: =>3^3x=3^3*3^2x-2

=>3x=2x+1

=>x=1

o: =>5^x*26=650

=>5^x=25

=>x=2

p: =>3^x-1=27

=>x-1=3

=>x=4

t: =>x+x-1+...+x-2018=0

=>2019x-2037171=0

=>x=1009

\(3^{x+1}+3^{x+3}=810\)

\(\Rightarrow3^x.3+3^x.27=810\)

\(\Rightarrow3^x\left(3+27\right)=810\)

\(\Rightarrow3^x.30=810\)

\(\Rightarrow3^x=27\Rightarrow x=3\)

`[101]`

`3^x . 3 + 3^x . 27 = 810`

`3^x . 30 = 810`

`3^x = 27`

`-> x = 3`.

X =3

\(\Leftrightarrow2^x\cdot\dfrac{9}{2}=9\cdot2^5\)

\(\Leftrightarrow2^x=2^6\)

=>x=6

`2^x(1/2 + 4) = 9 . 2^5`.

`[57]`

`2^x . 9/2 = 9 . 2^5`

`<=> 2^(x-1) . 9 = 2^5 . 9`

`<=> x - 1 = 5`

`<=> x = 6`

`1/2 . 2^x + 4 . 2^x = 9 . 2^5`

`=> 2^x . (1/2 + 4) = 288`

`=> 2^x . 9/2 = 288`

`=> 2^x       = 288 : 9/2`

`=> 2^x       = 64`

`=> 2^x        = 2^6`

`=> x             =6`

Vậy `x=6`

a) 2²²⁵ = (2³)⁷⁵ = 8⁷⁵

3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

Do 8 < 9 nên 8⁷⁵ < 9⁷⁵

Vậy 2²²⁵ < 3¹⁵⁰

b) Đọc ko được số nên ko giải

c) 3⁴⁰⁰ = (3²)²⁰⁰ = 9²⁰⁰

Do 200 < 2000 nên 9²⁰⁰ < 9²⁰⁰⁰

Vậy 3⁴⁰⁰ < 9²⁰⁰⁰

d) 2³³² = (2³)¹¹¹ : 2 = 8¹¹¹ : 2

3²²³ = (3²)¹¹¹.3 = 9¹¹¹.3

Do 8 < 9 nên 8¹¹¹ < 9¹¹¹

Suy ra: 8¹¹¹ : 2 < 9¹¹¹

Suy ra: 8¹¹¹ : 2 < 9¹¹¹ . 3

Vậy 2³³² < 9²²³

b) Ta có: 2 < 5 và 2 > 1

31 < 35

Suy ra 2³¹ < 3³⁵⁰

a: \(A=3^2\cdot3^3\cdot\dfrac{1}{3^4}\cdot3^2=3^3>a^2\)

b: \(B=2^2\cdot2^5:\dfrac{1}{2}=2^8>a^2\)

c: \(C=3^2\cdot2^5\cdot\dfrac{2^2}{3^2}\cdot2^7>a^2\)

5:

a: \(2^{225}=8^{75}< 9^{75}=3^{150}\)

c: \(3^{400}=\left(3^2\right)^{200}=9^{200}\)

d: \(9^{2000}=\left(9^5\right)^{400}>3^{400}\)