+738 hi guest! i'm not really sure if you meant \(5^{5x}+1=25^{2x}\) or \(5^{5x+1}=25^{2x}\), so I'll solve them both for you! :)
if you meant \(5^{5x}+1=25^{2x}\), then you can first start off by simplifying the equation.
\(5^{5x}+1=25^{2x} \)
\(5^{5x}+1=(5^2)^{2x}\)
\(5^{5x}+1=5^{4x}\)
this has equation has \(\boxed{\textbf{no solution}}\)
if you meant \(5^{5x+1}=25^{2x}\), then you can start off by simplifying again.
\(5^{5x+1}=25^{2x}\)
\(5^{5x+1}=(5^2)^{2x}\)
\(5^{5x+1}=5^{4x}\)
since the bases are the same, we can solve for the exponents by making them equal.
\(5x+1=4x\)
\(x+1=0\)
\(\boxed{x=-1}\)
i hope this helped you! :)
