Ta có: \(f\left(x+1\right)-f\left(x\right)=100\)
Thay \(y=f\left(x\right)=5^x\) vào ta có:
\(5^{x+1}-5^x=100\)
\(\Rightarrow5^x\cdot5^1-5^x=100\)
\(\Rightarrow5^x\cdot\left(5^1-1\right)=100\)
\(\Rightarrow5^x\cdot4=100\)
\(\Rightarrow5^x=25=5^2\)
\(\Rightarrow x=2\)