Question

5^2x+1.5^2x+2-5^x.5^3x+2=100

Answer 1

\(5^{2x+1}\cdot5^{2x+2}-5^x\cdot5^{3x+2}=100\)

\(\Leftrightarrow5^{4x+3}-5^{4x+2}=100\)

\(\Leftrightarrow625^x\left(5^3-5^2\right)=100\)

\(\Leftrightarrow625^x=1\)

hay x=0

Answer 2

\(\Rightarrow5^{2x+1+2x+2}-5^{x+3x+2}=100\\ \Rightarrow5^{4x+3}-5^{4x+2}=100\\ \Rightarrow5^{4x+2}\left(5-1\right)=100\\ \Rightarrow5^{4x+2}=25=5^2\\ \Rightarrow4x+2=2\Rightarrow x=0\)

Answer 3

\(5^{2x+1}.5^{2x+2}-5^x.5^{3x+2}=100\)

\(5^{4x+3}-5^{4x+2}=100\)

\(5^{4x+2}\left(5-1\right)=100\)

\(5^{4x+2}=25\)

4x+2=2

4x=0

x=0