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) Решите уравнение 5^5х+1 = 25^2х

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 Jun 29, 2020
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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! :)

 Jun 29, 2020

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