Give analytical solution

$\textbf{Put $\mathbf{x=2t}$ where $\mathbf{t\in \mathbb{R}$ }}\\\\ \textbf{We Get $\mathbf{5^t-(2)^{2t}=1\Leftrightarrow 5^t-4^t=1...........(1)}$}\\\\ \textbf{For $\mathbf{f(t)=5^t-4^t}$ is an Increasing function for $\mathbf{t>0}$ $}\\\\ \textbf{So These Two Curve Intersect at one Point.}\\\\ $\textbf{So only $\mathbf{t=1}$ Satisfies equation..(1) }\\\\ So $\mathbf{t=1\Leftrightarrow x=2}$\\\\ Not a Complete Solution\\\\ can Anyone Explain a Behaviour of $\mathbf{f(t)=5^t-4^t}$\\\\