Question

[Nguyễn Ngọc Lâm Uyên]

I/ Tìm x

a) ( x - 6 )³ = ( x - 6 )²

b) ( 7 . x - 11 )³ = 2⁵ . 5² + 200

c) 3 + 2^x-1 = 24 - [ 4² - ( 2² - 1 ) ]

II/ Tìm x \(\in\)N, biết:

a) 3^x . 3 = 243

b) 2^x . 16² = 1024

c) 64 . 4^x = 16⁸

d) 2^x = 16

III/ Viết các kết quả sau dưới dạng một lũy thừa

a) 125⁵ : 25³

b)  27⁶ : 9³

c)  4²⁰ : 2¹⁵

d)  24ⁿ : 2²ⁿ

e)  64⁴ . 16⁵ : 4²⁰

g)  32⁴ : 8⁶

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 Help với!!! Mik cần gấp lắm mai phải nộp rồi ;-;

Answer 1

[Trí Tiên亗]

a) \(\left(x-6\right)^3=\left(x-6\right)^2\Leftrightarrow\orbr{\begin{cases}x-6=1\Leftrightarrow x=7\\x-6=0\Leftrightarrow x=6\end{cases}}\)

b) \(\left(7.x-11\right)^3=2^5.5^2+200\)

\(\Leftrightarrow\left(7.x-11\right)^3=800+200\)

\(\Leftrightarrow\left(7.x-11\right)^3=1000\)

\(\Leftrightarrow\left(7.x-11\right)^3=10^3\)

\(\Leftrightarrow7x-11=10\Leftrightarrow7x=21\Leftrightarrow x=3\)

c) \(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\)

\(\Leftrightarrow3+2^{x-1}=24-\left[4^2-3\right]\)

\(\Leftrightarrow3+2^{x-1}=24-13\)

\(\Leftrightarrow3+2^{x-1}=11\)

\(\Leftrightarrow2^{x-1}=8\Leftrightarrow2^{x-1}=2^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)

Answer 2

[Trí Tiên亗]

a)\(3^x.3=243\Leftrightarrow3^x=81\Leftrightarrow3^x=3^4\Leftrightarrow x=4\)

b) \(2^x.16^2=1024\Leftrightarrow2^x.256=1024\Leftrightarrow2^x=4\Leftrightarrow2^x=2^2\Leftrightarrow x=2\)

c) \(64:4^x=16^8\Leftrightarrow4^x=67108864\Leftrightarrow4^x=4^{13}\Leftrightarrow x=13\)

d) \(2^x=16\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)