Question

tìm x

a) ( 7x - 11 )³ = 2⁵ . 5² + 200

b) x¹⁰ = 1^x

c) x¹⁰ = x

d) ( 2x - 15 )⁵ = ( 2x - 15 )³

e) 2 .3^x = 10 . 3¹² + 8 . 27⁴

Answer 1

a) (7x - 11)³ = 2⁵.5² + 200

=> (7x - 11)³ = 1000

=> (7x - 11)³ = 10³

=> 7x - 11 = 10

=> 7x = 10 + 11

=> 7x = 21

=> x = 21 : 7

=> x = 3 

Answer 2

b) x¹⁰ = 1^x

=> x¹⁰ = 1

=> x¹⁰ = 1¹⁰

=> x = 1

c) x¹⁰ = x

=> x¹⁰ - x = 0

=> x(x⁹ - 1) = 0

=> \(\orbr{\begin{cases}x=0\\x^9-1=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=0\\x^9=1\end{cases}}\)

=> \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

Vậy...

Answer 3

d) (2x - 15)⁵ = (2x - 15)³

=> (2x - 15)⁵ - (2x - 15)³ = 0

=> (2x - 15)³.[(2x - 15)² - 1] = 0

=> \(\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)

=> \(\orbr{\begin{cases}2x-15=0\\\left(2x-15\right)^2=1\end{cases}}\)

=>\(\orbr{\begin{cases}2x=15\\2x-15=\pm1\end{cases}}\)

=> x = 15/2

hoặc +) 2x - 15 = 1 (1)

        +) 2x - 15 = -1 (2)

Giải (1) : 2x - 15 = 1

 => 2x = 16

=> x = 8

Giải (2) : 2x - 15 = -1

=> 2x = 14

=> x = 7