Question

5^x + 5^{x + 2} + 5^{x + 4} = 3255
Tìm x

Answer 1

\(5^x+5^{x+2}+5^{x+4}=3255\)

\(\Rightarrow5^x\left(1+5^2+5^4\right)=3255\)

\(\Rightarrow5^x.651=3255\)

\(\Rightarrow5^x=5\Rightarrow x=1\)

Answer 2

\(5^x+5^{x+2}+5^{x+4}=3255\)

\(5^x+5^x.5^2+5^x.5^4=3255\)

\(5^x.\left(5^2+5^4+1\right)=3255\)

\(5^x.651=3255\)

\(5^x=3255:651\)

\(5^x=5\)

\(\Rightarrow x=1\)

Answer 3

\(5^x+5^{x+2}+5^{x+4}=3255\)

\(\Leftrightarrow5^x+5^2.5^x+5^4.5^x=3255\)

\(\Leftrightarrow5^x.\left(1+5^2+5^4\right)=3255\)

\(\Leftrightarrow5^x.651=3255\)

\(\Leftrightarrow5^x=5=5^1\)

\(\Leftrightarrow x=1\)