Question

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Answer 1

k) 5^x + 5^x+1 + 5^x+2 = 775

=> 5^x . ( 1 + 5 + 5² ) = 775

=> 5^x . ( 1 + 5 + 25 ) = 775

=> 5^x . 31 = 775

=> 5^x = 775 : 31 = 25

=> 5^x = 5²

=> x = 2

Answer 2

l) ( 7x - 11 )³ = 2⁵ . 5² + 200

=> ( 7x - 11 )³ = 32 . 25 + 200

=> ( 7x - 11 )³ = 800 + 200

=> ( 7x - 11 )³ = 1000

=> ( 7x - 11 )³ = 10³

=> 7x - 11 = 10

=> 7x = 10 + 11 = 21

=> x = 21 : 7 = 3

Answer 3

k) \(5^x+5^{x+1}+5^{x+2}=775\)

\(\Leftrightarrow5^x.\left(1+5^1+5^2\right)=775\)

\(\Leftrightarrow5^x.31=775\)

\(\Leftrightarrow5^x=775\div31\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow5^x=5^2\)

\(\Leftrightarrow x=2\)

Answer 4

k) \(5^x+5^{x+1}+5^{x+2}=775\)

\(\Leftrightarrow5^x.\left(1+5+25\right)=775\)

\(\Leftrightarrow5^x.31=775\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow x=2\)

Vậy \(x=2\)

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

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

\(\Leftrightarrow7x-11=10\)

\(\Leftrightarrow7x=21\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

Answer 5

h) ( 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