Question

tìm x

\(5^x+5^{x+1}+5^{x+2}=775\)

Answer 1

\(5^x+5^{x+1}+5^{x+2}=775\)

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

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

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

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

\(\Rightarrow5^x=775:31=25=5^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

Answer 2

5^x + 5^{x + 1} + 5^{x + 2} = 775

5^x . 1 + 5^x . 5 + 5^x . 25 = 775

5^x . (1 + 5 + 25) = 775

5^x . 31 = 775

5^x       = 775 : 31

5^x       = 25

5^x       = 5²

Suy ra : x = 2